I see a couple of good answers were posted while I was writing, but here are my thoughts anyway
The verse you're looking for, Andy, is Jeremiah 49:38.
"'I will set My throne in Elam, and will destroy from there the king and the princes,’ says the Lord."
This possibly could refer to the millennial reign, but not necessarily so. From Jeremiah 46 to 51, the prophet is relating God's coming judgements on each of the nations that have troubled Jerusalem and the Southern Kingdom. Taken together, these judgments are to prove God's successfully over each pagan nation: they may seem to flourish according to their individual wills, but they are, in fact, subject to God Himself.
In Jeremiah 49:34-39, God speaks specifically of His judgment on Elam. First, He says He will break the military might of Elam (v35). Then He says He will scatter its people across the planet (v36). He states He will absolutely destroy all of Elam's power and will replace it with His own (vv37-39).
This must be read in the context of chapters 46 to 51: specifically, as I said, that God is assuring the people of Judah that He is indeed greater than their enemies and that those enemies will each be judged for their actions against His people. Does it necessarily person to the MK? That is a question of interpretation. Take verse 39.
"‘But it shall come to pass in the latter days:I will bring back the captives of Elam,’ says the Lord.”
Ignoring whether the Hebrew word translated here means "captives" or" fortunes" --it all depends on the vowel points which are not present in the earliest manuscripts (for the record, given the context, I believe captives is correct)-- but, ignoring that point of uncertainty, what is certain is that this will occur in "the latter days." The expositor needs to determine whether the "latter days" refers to the MK, or to some period leading up to --and possibly including-- the days of God's Wrath being poured out on the earth, which precedes the MK.
@Jedidjah has given a very useful technique for the student of Scripture.
