Smalling excelled during a loan spell at Roma last season, and the Italian giants have said on a number of occasions that they are keen to sign the Englishman on a permanent deal.
The 30-year-old is back with United, but he has been left out of the squad for their first two matches of the 2020-21 campaign against Crystal Palace and Luton Town as the transfer speculation continues to gather pace.
According to The Guardian, Roma have already had an £11m bid rejected but are preparing to launch a second offer for a player valued at £18m by the 20-time English champions.
Smalling, who has also been linked with Inter Milan, still has two years left to run on his contract at Old Trafford.
There also remains uncertainty surrounding the future of Marcos Rojo, while injury problems for Phil Jones and Axel Tuanzebe has seen 18-year-old Teden Mengi promoted to the United first team on a permanent basis. body check tags ::