I believe the Antichrist will be a Gentile, because he is the final ruler of the Gentile kingdoms of the world. He will appear in the end times as the head of the Gentile world powers. All the rulers of the Gentile world powers in Daniel 2 & 7 were Gentiles. Since the Antichrist will be a great persecutor of the Jews, it is highly unlikely that he will be a Jew. In Revelation 13: 1, his origin is symbolically described as coming up out of the sea. Sea when used symbolically in Scripture stands for the Gentile nations of the world (see Revelation 17:15). The fact that he comes up out of the sea would be describing his gentile origin.
The Bible does not tell us specifically of his origin or who the Antichrist will be. Paul reminds us that the Antichrist will not be revealed until after the Rapture of the Church (2 Thessalonians 2:3-5).