Smalling made the move to Italy after United’s £80m deal to sign Harry Maguire from Leicester meant he was surplus to requirements at Old Trafford.
The club paid an initial £2.7m to secure the loan deal and Smalling has established himself as an important part of Paulo Fonseca’s team.
After initially struggling with a muscle injury, the 29-year-old has done enough to persuade the Serie A giants to sign him permanently.
Smalling has formed an effective partnership with Gianluca Mancini, starting the last three league games ahead of Federico Fazio and Juan Jesus.
According to Italian journalist Gianluca di Marzio, Roma are keen to open talks with United and Smalling has previously suggested he is keen to stay in Italy.
When he first joined Roma, Smalling said: “This is the perfect opportunity for me.
“The chance to experience a new league, with a big team that has got big aspirations is exactly what I needed.
“Hopefully I can hit the ground running.
“This is an opportunity that came to me that I was very interested in, and I was very eager to come.
“It happened very quickly and now I focus on the next game, getting up to speed with training in terms of the manager’s methods and then hopefully have a very good season.
“To be able to have the chance at a big club, and then if it prolongs and the club is happy then I can definitely see a longer-term future in Italy.”
An agreement between the two clubs looks likely given the number of centre-back options United have at their disposal.
Along with first-choice pairing Maguire and Victor Lindelof, manager Ole Gunnar Solskjaer also has Eric Bailly, Phil Jones, Marcos Rojo and Axel Tuanzebe to call on.