Second, Jesus’ disciples understood that He was speaking about John the Baptist, since Elijah appeared on the Mount of Transfiguration ( Matt. 17:10–13 ). Since John had already lived and died by then, and since Elijah still had the same name and self consciousness, Elijah had obviously not been reincarnated as John the Baptist.
Third, Elijah does not fit the reincarnation model for another reason—he did not die. He was taken to heaven like Enoch, who did not “see death” ( 2 Kings 2:11 ; cf. Heb. 11:5 ). According to traditional reincarnation, one must first die before he can be reincarnated into another body.
Fourth, if there is any doubt about this passage, it should be understood in the light of the clear teaching of Scripture opposing reincarnation. Hebrews, for example declares, “it is appointed for men to die once, but after this the judgment” (Heb. 9:27; cf. John 9:2)."
Norman Geisler And Thomas A. Howe, When Critics Ask: A Popular Handbook on Bible Difficulties