Reynolds, 19, has drawn interest from Juventus, Club Brugge and another unnamed club during the January transfer window, but Roma are now in pole position and sources have told ESPN they are optimistic of confirming the move next week.
Roma are set to pay FC Dallas a fee in the region of €8 million plus add-ons for Reynolds and and he will initially join the Serie A side on loan.
Juventus were close to signing Reynolds earlier in the window but encountered complications due to having filled their non-EU allowance for this season. There were talks of Juventus signing Reynolds and then loaning him to Benevento, but that move stalled.
Sources told ESPN Club Brugge then came back in with an improved offer but Roma have moved to the front of the queue and are optimistic of getting the deal over the line.
Reynolds was part of this month's U.S. Under-23 roster but withdrew due to personal reasons on Jan. 19.