Ole Gunnar Solskjaer confirmed a deal was close on Friday, with Smalling having travelled to Italy to finalise a transfer to the Stadio Olimpico.
Smalling made 24 Premier League appearances last season, though with Harry Maguire's arrival for a record fee, the 29-year-old has been allowed to leave, having not made an appearance so far this campaign.
The move now looks to be nearing completion, with Roma posting pictures of Smalling undergoing his medical on their official Twitter account.
Smalling's departure comes after Alexis Sanchez joined Roma's Serie A rivals Inter on loan, while Matteo Darmian is also set to sign for Parma, though the former Fulham centre-back could still have a future at Old Trafford, according to Solskjaer.
"There haven't been a lot of English players in Italy. I think he'll enjoy the experience and I'm sure he'll come back stronger and better for it," Solskjaer told a news conference earlier on Friday.