In his commentary C.K. Barrett states the "Greeks" are Gentiles:
Ἕλληνές τινες. The word Ἕλλην signifies not one strictly of the Greek race but one of non-Jewish birth. Cf. 7.35 and see Mark 7.26, where a woman first described as a "Greek" (Ἑλληνίς) is further defined as a Syro-Phoenician. These Greeks are mentioned here and in the next verse, and then heard of no more; the narrative proceeds without them. They speak as representatives of the Gentile Church to which john and his readers belong.
The two verses he references:
The Jews said to one another, “Where does this man intend to go that we will not find him? Does he intend to go to the Dispersion among the Greeks and teach the Greeks? (John 7:35) [ESV]
Now the woman was a Gentile, a Syrophoenician by birth. And she begged him to cast the demon out of her daughter. (Mark 7:26)
This follows a distinction in the New Testament between Ἕλλην which "embraces all nations not Jews that made the language, customs, and learning of the Greeks their own" and Ἑλληνιστής "used in the NT of Jews born in foreign lands and speaking Greek" (e.g. Acts 6:1, 9:29, 11:20).
Other commentators also see the meaning as Gentiles. For example, Joseph Benson says:
John 12:20-22. And there were certain Greeks — A prelude of the Gentile Church. The phrase, τινες Ελληνες, here used, signifies properly, as translators have rendered it, certain Greeks. But all the Gentiles being thus named by the Jews, it was intended to denote their religion, rather than their country: they had been brought up heathen: they were not, however, now idolatrous Gentiles, but proselytes to the Jewish religion, and worshippers of the true God, persons who had come to Jerusalem, it seems, on purpose to worship him; but that they had been circumcised is not certain.
Likewise in his paper on John 12:20 Johannes Beutler writes:
...unlike some of the passages where the allusion to gentiles is at least doubtful, in our text this meaning seems to be beyond doubt.
Beutler's makes the case John 12:20 is drawn from the LXX Isaiah 52:15:
so shall many nations be astonished at him, and kings shall shut their mouth, because those who were not informed about him shall see and those who did not hear shall understand.
(Isaiah 52:15 NETS)
The wording of the approach of the Greeks to Jesus echoes in an astonishing way Isa 52,15 LXX:
οὕτως θαυμάσονται ἔθνη πολλὰ ἐπ᾽ αὐτῷ
καὶ συνέξουσιν βασιλεῗς τὸ στόμα αὐτῶν
ὅτι οἷς οὐκ ἀνηγγέλη περὶ αὐτοῦ ὄψονται
καὶ οἳ οὐκ ἀκηκόασιν συνήσουσιν
This agrees with the overall context which begins with the Pharisees saying the whole world (not just Greek speaking Jews) has gone after Jesus (v. 19) and Jesus saying He will draw all people (not only the Jews) to Himself (v. 32).
1. C.K. Barrett, The Gospel According to St. John, S.P.C.K, 1962, p. 351
2. Benson Bible Commentary
3. Johnnes Beutler, "Greeks Come to See Jesus (John 12,20f)", Biblica, Vol. 71 No. 2 (1990). p. 342