Nicodemus Should Have Known from the Old Testament
That the Old Testament is the source of the doctrine is confirmed by Christ Himself, for Nicodemus was supposed to have known these things. A slightly larger context helps see this:
Jn 3:3-10 (NKJV)
3 Jesus answered and said to him, “Most assuredly, I say to you,
unless one is born again [or "born from above," see below], he cannot see the kingdom of God.”
4 Nicodemus said to Him, “How can a man be born when he is old? Can he
enter a second time into his mother’s womb and be born?” 5 Jesus
answered, “Most assuredly, I say to you, unless one is born of water
and the Spirit, he cannot enter the kingdom of God. 6 That which is
born of the flesh is flesh [i.e. of woman], and that which is born of the Spirit is
spirit [i.e. of God]. 7 Do not marvel that I said to you, ‘You must be born again.’
8 The wind blows where it wishes, and you hear the sound of it, but
cannot tell where it comes from and where it goes. So is everyone who
is born of the Spirit.” 9 Nicodemus answered and said to Him, “How can
these things be?” 10 Jesus answered and said to him, “Are you the
teacher of Israel, and do not know these things?
Verse 10 clearly indicates that Christ expected that Nicodemus should be following Christ's previous statements because he was one of those that taught Israel the scriptures. So the concept certainly is not "new" with Jesus, but rather one contained in Israel's teachings. However, that does not mean it is found as directly stated in the OT as what Christ is stating here.
Clarifying Christ's Meaning
So Christ introduces the "born again" concept to the discussion and links it to the Jewish expectation of the kingdom of God (v.3). The phrase "born again" in the Greek is two words.
The first word is that typically used for ones birth, an aorist passive form of the verb γεννάω (gennáō), to "be born" (BDAG).1
The second word is ἄνωθεν (ánōthen), translated in the NT only in John 3:3 and 3:7 as "again." In most uses of the NT, it means "from above" (including Jn 3:31; also Jn 19:11; Jam 1:17, 3:15, 3:17) or "from the top" (Mt 27:51; Mk 15:38; Jn 19:23). Occasionally it is a time reference (in context), and so "from the first" or "from the beginning" (Act 26:5). The Luke 1:3 usage is debated whether it should be a time reference or a source from above reference. Gal 4:9 it is usually untranslated, considered to be intensifying the typical word for "again" in that passage, πάλιν (pálin).
It is (1) the fact that Christ does not use the common word for "again," πάλιν, in John 3, and (2) his paralleling of flesh/Spirit as sources of the two births that leads me to believe the better translation in all of John 3 is that used in v.31, "from above." The idea of "again" was probably favored because of Nicodemus' reply in v.4, where a repetition of a natural birth is inquired about (but even so, such is to him obviously an incredulous idea.
So the "born from above" Christ is referring to is a Spiritual birth, as he clarified in vv.5-8.
Therefore, to look for what Christ was referring to in the OT, we need to find references that (1) refer to the insufficiency of the fleshly birth, and (2) the necessity of the spiritual birth, especially as relates to the kingdom of God.
The Need and Remedy are both Understood in Job
The idea that the first, natural birth from a woman is insufficient is expressed in the book of Job.
Job 15:14—“What is man, that he could be pure?
And he who is born of a woman, that he could be righteous? (cf. Job 4:17)
Job 25:4—How then can man be righteous before God? Or how can he be pure who is
born of a woman?
Through these rhetorical questions, both righteousness and purity are understood to be impossible for one merely "born of a woman."
But Elihu gives the answer to these questions in his statement to Job:
23 “If there is a messenger for him,
A mediator, one among a thousand,
To show man His uprightness,
24 Then He is gracious to him, and says,
‘Deliver him from going down to the Pit;
I have found a ransom’;
25 His flesh shall be young like a child’s,
He shall return to the days of his youth.
26 He shall pray to God, and He will delight in him,
He shall see His face with joy,
For He restores to man His righteousness.
27 Then he looks at men and says,
‘I have sinned, and perverted what was right,
And it did not profit me.’
28 He will redeem his soul from going down to the Pit,
And his life shall see the light.
29 Behold, God works all these things,
twice, in fact, three times with a man,
30 To bring back his soul from the Pit,
That he may be enlightened with the light of life.
Notice how the theme in this passage also parallels Christ's later statement in John 3 about his death. He is the "mediator" to "show man His uprightness" of Job 33:23. He is the "ransom" found (v.24). Through this mediator, one is made new from above, both physically (flesh, v.25) and spiritually (righteousness, v.26), which newness comes by a person's repentance (v.27) and is a redeeming from the spirit going down into the pit (i.e. grave, v.28), and a bringing of the flesh "back" from the grave (v.30).
Note the similar themes between Job 33 and John 3 (some of these connections are more direct, some more conceptual... I leave it for each one reading to decide how well matched conceptually the parallels I show are):
Job 33:23-30 John 3
A messenger v.23 Christ's witness v.11, v.32-34
A mediator v.23 The Son from heaven as mediator v.13-16
Show uprightness v.23 Christ recognized as godly v.2, above all v.31
Deliverance from pit v.24 No perishing v.15, salvation v.17
Ransom v.24 Son is given v.16
Flesh like a child's v.25 Born again v.3-8
Return to youth v.25 Born again v.3-8
Redeemer prays to God v.26 [no parallel found]
God delights in Redeemer v.26 God with Christ v.2, loves Son v.35
Restores righteousness v.26 Believer not condemned v.18
Admission of unrighteousness v.27 Belief is key v.15-16, 18, 33
Redemption from going into Pit v.28 Believers not perish, have eternal life v.15, 36
Redeemed one's life sees light v.28 Doers of truth go to light v.21
Three works of God for man v.29 [no parallel found]*
Redemption back from the Pit v.30 [no parallel found]**
Enlightenment by life v.30 Doers of truth deeds enlightened v.21
* Unless the three works are as messenger, mediator, and judge, all ideas seen in both
Job and John
** Resurrection is not forefront in John 3, but both the concept of eternal life
(v.15-16, 36) and experiencing the kingdom (v.3, 5) have that as a background necessity.
While exploring potential parallels between Job 33 and John 3 is intriguing, for the question here, the passage in Job (especially v.25) is speaking of a change like a new birth, and it ties to the resurrection from the grave (v.30). These ideas are tied more directly to the Spirit and kingdom in later revelation...
The Picture in Ezekiel
Ezekiel 37 speaks of the resurrection, which Job tied to the new birth, but in Ezekiel it is clear that it is an act of the Spirit (the same word in Hebrew for "breath," רוּחַ [rûaḥ]). The term is found in v. 1, 5, 6, 8, 9, 10, 14, but specifically the active agent of physical resurrection (v.5-8), and a renewing of spirit itself (v.9-10, 14).
Further, this resurrection pictured in Ezekiel 37 is part of Israel being put back into their land (v.14), united (v.15-21), and the ushering in of the one kingdom under one king (v.22), never to be defiled again (v.23)—that is, to remain righteous.
The "born from above" concept was already taught within the OT canon of Christ's day. It was scattered in various passages, of which there are others that could be mentioned, but the two above bring together the concepts. Job shows the need for new birth, that new birth bringing both a spiritual change (righteousness) and physical change (resurrection). Ezekiel shows a spiritual source of the resurrection, a spiritual change as well, and the resurrection being needed for experiencing the kingdom.
1 BDAG refers to William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000).