And Melchizedek king of Salem brought forth bread and wine:
and he was the priest of the most high God.
And he blessed him, and said,
Blessed be Abram of the most high God, possessor of heaven and earth:
And he gave him tithes of all.
Genesis 14:18-20
Who was this priest of the Most High God at Salem? (Salem later is thought to have become Jerusalem). Apparently there were more people than just Abram worshipping the true God.
Melchizedek probably wasn't Noah.
Noah (who lived 350 years after the flood) was still alive when Abram was born.
Abram was born 292 years after the flood.--BUT---he wasn't "called" by God to leave his home until he was 75. That would be 367 years after the flood.
Was it Shem? Shem lived 500 years past the flood. So it's possible. But who knows.
The following verse MIGHT indicate it was Shem (in this case Melchizedek is a "type" for Christ). Shem would make sense since of the living at the time, his lineage would stretch back before the line of demarcation of the post-flood living to before the flood, symbolically as if he had no beginning. Also, living the longest after the flood, outliving his son Arphaxad, grandson Salah, great grandson Eber & only dying the year before his great great grandson Peleg. So to many, including Abram at the time, he would seem to have no end.
For this Melchisedec,
king of Salem,
priest of the most high God,
who met Abraham returning from the slaughter of the kings,
and blessed him;
Without father, without mother, without descent,
having neither beginning of days, nor end of life;
but made like unto the Son of God;
abideth a priest continually.
Hebrews 7:1,3
As for Melchizedek as a type for Christ, the anti-type:
The LORD said unto my Lord, Sit thou at my right hand,
Thou art a priest for ever after the order of Melchizedek.
Psalm 110:1,4