ἐγώ εἰμι with predicates
The Fourth Gospel records Jesus saying ἐγώ εἰμι with a predicate twelve times (6:35, 6:48, 6:51, 8:12, 10:7, 10:9, 10:11, 10:14, 11:25, 14:6, 15:1, 15:5). These help demonstrate what language Jesus spoke because "Hebrew does not have a word for the present tense of the verb "to be." In other words, there is no Hebrew word for "am" or "is" or "are." Therefore, in order to say "I am Joseph," for example, one would say "Ani Joseph" ("I Joseph")."1
Therefore, if Jesus spoke Aramaic, the proper rendering into Greek would be "I ---" (not "I am ---").
In fact, the Semitic form is found in John the Baptist's testimony:
He said, “I am the ‘voice of one shouting in the wilderness: “Make-straight the way of the Lord”’, just as Isaiah the prophet said [in Isa 40:3]”. (John 1:23 DLNT)
ἔφη ἐγὼ φωνὴ βοῶντος ἐν τῇ ἐρήμῳ εὐθύνατε τὴν ὁδὸν κυρίου καθὼς εἶπεν Ἠσαΐας ὁ προφήτης
From Luke (1:5) the Baptist is identified as a Levitical priest; undoubtedly schooled in Hebrew and was speaking to other priests and Levities (1:19). At first blush the Baptist spoke in Hebrew or Aramaic which the writer translated literally into Greek. Yet the Gospel also records (1:20-21) he used εἰμι which has no Semitic counterpart. So the better explanation is the Baptist chose the Semitic expression even though he spoke in Greek. Perhaps he was "accustomed to think and speak in Aramaic as well as in Greek."2
This would also explain why his quote follows neither the LXX or the Hebrew text. He replaced ἑτοιμάσατε with εὐθύνατε in order to conflate either ἑτοιμάσατε, εὐθείας of the LXX or פנו ,ישרו of the Hebrew into a single action.
Another reason would be to avoid saying "ἐγώ εἰμι..." altogether. The LXX of second Isaiah has that expression for God speaking fifteen times (41:4; 43:10, 25; 45:8, 18, 19, 22; 46:4, 9; 47:8, 10; 48:12, 17; 51:12; 52:6) occasionally with a predicate:
and remember the former things of old, because I am God, and there is no other beside me. (LXX-Isaiah 46:9)
καὶ μνήσθητε τὰ πρότερα ἀπὸ τοῦ αἰῶνος ὅτι ἐγώ εἰμι ὁ θεός καὶ οὐκ ἔστιν ἔτι πλὴν ἐμοῦ
The LXX adds the implied verb when God self-identifies with a predicate (I God). A Levite versed in both the Hebrew and Greek texts would understand the potential for a charge of blasphemy when quoting Isaiah and saying ἐγὼ εἰμι... Therefore, using the Semitic I voice... despite speaking Greek eliminates the potential of a claim of blasphemy against the Baptist.3
Regardless of the reason, the manner in which the Gospel presents the Baptist's witness shows the writer had no qualms omitting εἰμι to write I voice; nor should there be question the reader would find this unintelligible. So, if Jesus spoke either Hebrew or Aramaic when saying "I am ----" (with a predicate), the writer should continue to reflect that Semitic form. The reader expects, "I the bread of life" (ἐγώ ὁ ἄρτος τῆς ζωῆς) for example. The fact εἰμι is always used when made with a predicate is best explained by understanding they were spoken in Greek.
ἐγώ εἰμι in John 8
In terms of the entire Gospel, Chapter 8 appears to be the centerpiece of the writer's presentation of ἐγώ εἰμι spoken by Jesus. The passage begins with a predicate use and is followed by three absolute uses the last of which are Jesus' final words:
Again Jesus spoke to them, saying, “I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life.” (John 8:12) [ESV]
Πάλιν οὖν ὁ Ἰησοῦς αὐτοῖς ἐλάλησεν λέγων,Ἐγώ εἰμι τὸ φῶς τοῦ κόσμου· ὁ ἀκολουθῶν ἐμοὶ οὐ μὴ περιπατήσει ἐν τῇ σκοτίᾳ ἀλλ᾽ ἕξει τὸ φῶς τῆς ζωῆς
I told you that you would die in your sins, for unless you believe that I am he you will die in your sins.” (John 8:24)
εἶπον οὖν ὑμῖν ὅτι ἀποθανεῖσθε ἐν ταῖς ἁμαρτίαις ὑμῶν ἐὰν γὰρ μὴ πιστεύσητε ὅτι ἐγώ εἰμι ἀποθανεῖσθε ἐν ταῖς ἁμαρτίαις ὑμῶν
So Jesus said to them, “When you have lifted up the Son of Man, then you will know that I am he, and that I do nothing on my own authority, but speak just as the Father taught me. (John 8:28)
εἶπεν οὖν αὐτοῖς ὁ Ἰησοῦς ὅταν ὑψώσητε τὸν υἱὸν τοῦ ἀνθρώπου τότε γνώσεσθε ὅτι ἐγώ εἰμι καὶ ἀπ᾽ ἐμαυτοῦ ποιῶ οὐδέν ἀλλὰ καθὼς ἐδίδαξέν με ὁ πατὴρ ταῦτα λαλῶ
Jesus said to them, “Truly, truly, I say to you, before Abraham was, I am.” (John 8:58)
εἶπεν αὐτοῖς Ἰησοῦς ἀμὴν ἀμὴν λέγω ὑμῖν πρὶν Ἀβραὰμ γενέσθαι ἐγὼ εἰμί
Jesus begins the discussion with "ἐγώ εἰμι τὸ φῶς τοῦ κόσμου" I am the light of the world. As discussed above, if Jesus was speaking in Hebrew or Aramaic, the Semitic form would be, ἐγώ τὸ φῶς τοῦ κόσμου. So ἐγώ εἰμι τὸ φῶς τοῦ κόσμου shows Jesus spoke in Greek.
In discussing verse 8:24 C.K. Barrett arrives at that same conclusion:
The absolute use of ἐγώ εἰμι at 6.20; 18.6...can readily be understood from the context; here however it seems impossible to supply an appropriate complement from the context. Moreover the question that follows (σὺ τίς εἶ; v. 25) suggests that the words were not plain to the hearers. ἐγώ εἰμι without compliment (see also vv. 28, 58 and 13.19) is hardly a Greek expression. It occurs not infrequently in the LXX and on this basis (rather than on direct translation by John of a Semitic original) the words should be understood. In the LXX they render אני הוא ('ani hu', literally "I (am) he"), which occurs especially in the words of God himself, and there is a particularly close parallel to the present passage in Isaiah 43.10, ἵνα γνῶτε καὶ πιστεύσητε καὶ συνῆτε ὅτι ἐγώ εἰμι (אני הוא).4
He goes on to say (see below) εἰμι is properly a continuous tense implying neither beginning nor end, which fits 8:58:
πρὶν Ἀβραὰμ γενέσθαι. Before Abraham came into existence; perhaps, before Abraham was born, since γενέσθαι can have this meaning. ἐγώ εἰμι...The meaning suggested in the note there suits admirably the present context: Before Abraham came into being, I eternally was, as now I am, and ever continue to be.5
Where the first three uses may "mask" ἐγώ εἰμι to some extent, first with a predicate then within a statement where the meaning might be considered as normal speech (cf. John 9:9), 8:58 ends with ἐγὼ εἰμί and the meaning cannot be mistaken (as the crowd's reaction demonstrates).
The Old Testament Source
If the origin of the expression is from the LXX, its Semitic form cannot be dismissed. In other words, it is most unlikely an LXX use of ἐγώ εἰμι which does not directly correspond to the Hebrew (either אני הוא ’ănî hū' or אנכי אנכי הוא ’ānōḵî ’ānōḵî hū') could be a "source" text for the Gospel writer. Similar to the Baptist's Greek confession, the underlying concern is the Hebrew Scripture. For this reason, Exodus 3:14 should be eliminated as a source for the writer (although it is possible the crowd made that connection). Additional support for eliminating Exodus 3:14 is found in Richard Bauckham's observation that the number of absolute uses of ἐγώ εἰμι in the Gospel (9 which could be counted as 7) matches exactly that in the Hebrew text.6
Barrett identifies John 8:24 with LXX-Isaiah 43:10:
Similar passages occur at Deuteronomy 32.39; Isaiah 41:4; 43.13; 46.4; 48.12. In the Isaiah passages the meaning of the Hebrew is apparently "I am (forever) the same" with perhaps an allusion to the name יהוה (YHVH) given in Exodus 3:14-16;...The context demands a similar meaning for the Greek, though ἐγώ εἰμι is in itself (as Greek) a meaningless expression. The Lord, the first and with the last, is the eternal one. The εἰμι, that is to say, is a properly continuous tense, implying neither beginning nor end of existence. This meaning is particularly appropriate to v. 58 (where see the note), and appropriate also to the present verse, where it reinforces the assertion that Jesus belongs to the eternal heavenly world (ἐκ τῶν ἄνω). We may say then that ἐγώ εἰμι, thus understood, (i) indicates the eternal being of Jesus; (ii) thereby, and in itself, places Jesus on a level with God (ἐγώ εἰμι usually is found in the LXX on the lips of God himself; at Isaiah 47.8; Zephaniah 2.15 it is arrogantly used by men who put themselves in the place of God; and both אני and הוא were used as divine names-7
Barrett also states parataxis is one of the most striking feature of John's style.8
If the absolute uses in the Gospel (4:26, 6:20, 8:24, 8:28, 8:58, 13:19, 18:5, 18:6, 18:8) are arranged side-by-side with their order in the Hebrew Scripture, Isaiah 43:10 corresponds to the use in 8:24:

Other parallels are apparent as well. For example, the one spoken to the Samaritan woman and the one in Deuteronomy, the only one in the Pentateuch. This comparison would make Isaiah 43:25 as the specific source for 8:58:
“I, I am he
who blots out your transgressions for my own sake,
and I will not remember your sins. (Isaiah 43:25)
Verse 25 could be paraphrased, from the beginning and continuing forever, I, I am the one who blots out transgressions and forgets sin, for My own sake. This alludes back to the first use at 8:24: unless you believe I am you will die in your sins. Also the double "I" (אנכי אנכי הוא ’ānōḵî ’ānōḵî hū') of the passage acts in support of Jesus' claim to be one with the Father (cf. 10:30) an act which also elicits the response of stoning (cf. 10:33).
Conclusion
- The internal evidence of the Gospel shows Jesus began by saying "I am the light of the world" speaking Greek and there is no reason to believe He changed to Hebrew or Aramaic.
- ἐγώ εἰμι may be used in normal conversation, but it is obvious those who heard Jesus say "ἀμὴν ἀμὴν λέγω ὑμῖν πρὶν Ἀβραὰμ γενέσθαι ἐγὼ εἰμί" did not understand it as such. Their reaction, picking up stones to throw at Him, is the response to blasphemy.
- The origin of the expression is the LXX, but the Gospel writer understands the source as a Hebrew text. This eliminates Exodus 3:14.
- Any Hebrew text could be taken and, in fact all apply to Jesus. Yet the Gospel writer invites the reader to compare each use in the Gospel with a corresponding use in the OT. In this case Isaiah 43:25 corresponds to "Before Abraham existed, I am."
Notes:
- Dennis Prager, Exodus: God, Slavery, and Freedom, Regnery Faith, 2018, pp. 44
- C.K. Barrett, The Gospel According to St. John, S.P.C.K, 1962, p. 11
- The group of priests and Levites from Jerusalem asking "Who are you?" suggests a delegation sent for legal purposes; surely they knew of his miraculous birth and actual identity.
- Barrett, pp. 282-283
- Barrett, p. 292
- Richard Bauckham, The Testimony of the Beloved Disciple, Baker Academic, 2007, p. 247
- Barrett, p. 283
- Barrett, p. 6