Within some (mainly Protestant) circles, there is the theory that the figure of Melchizedek in Gen 14:18 is none other than the premortal Jesus; in other words, Melchizedek represents an Old Testament “Christophany.”
Latter-day Saints sometimes encounter this applied to the figure of Melchizedek in Gen 14:18 to answer the counter-charge to LDS claims of the nature of the priesthood, that is, “if Jesus is the only holder of the Melchizedek Priesthood, what about Melchizedek himself?” Some anti-Mormons who have advocated this view to respond to LDS claims would include Marian Bodine, Ron Rhodes, and James R. White.
However, as with so many arguments one finds from the above critics, when one investigates such claims, one discovers that it is based on eisegesis of the reason why Melchizedek is discussed with reference to Christ.
Interestingly, one of, if not the earliest, individuals to make this association was Ambrose of Milan (fans of The Simpsons [back when it was good] will know him as the one who converted Augustine of Hippo). However, the underlying theological reasons why Ambrose made this association would be anathema to White et al! Why? Ambrose, as all commentators on his theology of the Eucharist would agree, held that the Eucharist was a sacrifice and that Christ was substantially present in the sacrifice. The association of Jesus with the Melchizedek was tied into the sacrifice of the New Covenant (the “Mass” in Catholic circles) being prefigured by the sacrifice of Melchizedek whom offered bread and wine in Gen 14:18 (cf. Exposition of the Christian Faith Book 3 chapter XI).
Latter-day Saints have never claimed that Melchizedek and Jesus are one and the same person, and for good reason—there is not Scriptural justification for this identification. Within uniquely LDS scriptural texts, the person of Melchizedek and Jesus are differentiated from one another (Alma 13 and D&C 107 are pretty explicit in this). Furthermore, the epistle to the Hebrews itself differentiates between Melchizedek and Jesus wherein an identification of persons would violate the law of the Identity of Indiscernibles (e.g. Heb 7:3, 15). As the following quote from Jesuit scholar, Albert Vanhoye in his (excellent) commentary on Hebrews states correctly, the association of Melchizedek and Jesus in Hebrews is not an identification of persons, but one of prefiguration:
[The figure of Melchizedek in Psa 110] corresponds . . .to an image of the Son of God, for the Son of God has “neither beginning of days, nor end of life,” and only the Son of God could become “priest for ever.” With all these traits, the biblical image of Melchisedek constitutes a prefiguration of the glorified Christ, one of God and priest for ever. Only a prefiguration, because Melchisedek was not really Son of God, nor priest for ever; he was only “made like the Son of God” by the way he is represented in the text of Genesis, and not in reality. Likewise, his priesthood is not truly eternal but has only, in the text of Genesis, an appearance which has something of eternity about it. To express this important nuance, the author avoids using, concerning Melchisedek, the expression of the psalm, “for ever,” but uses an expression with a weaker sense, which can be translated as “continually” or “in perpetuity.” Of whom exactly, is Melchisedek a prefiguration? He is not a prefiguration of the Son of God before the incarnation, for the latter is not “without father,” he has God as father, and he is not a priest, for he lacks the fraternal link with mankind. Nor is Melchisedek a prefiguration of the incarnate Son of God and living his earthly life, because then he is not “without mother.,” he is the son of Mary; he is not “without genealogy,” being of the tribe of Juda. And he has not yet been proclaimed priest by God. Melchisedek is the prefiguration of the risen Christ, for the resurrection is a new creation, in which neither human father, nor human mother, nor genealogy have any part. The human nature of the risen Christ is the “the greater and more prefect tent, not made by hand of man, that is to say not of this creation” (Heb 9:11) by means of which Christ entered into intimacy with God and ran into God’s eternity. In the resurrection, the human nature of Jesus received the fullness of filial glory but that glory does not break the links of Christ with mankind, for it is through the complete fraternal solidarity with them that it was obtained (see Heb 2:9-18). It follows that the glorified Christ, Son of God and brother of mankind, is “priest for ever.” That is what the author sees prefigured in the biblical image of the perpetual priesthood of Melchisedek.
Albert Vanhoye, A Different Priest: The Epistle to the Hebrews (Miami: Convivium Press, 2011), 209-10.