The 30-year-old joined Roma on loan last summer and has impressed for the Italian outfit during the 2019-20 season, making 28 appearances in all competitions.
The Serie A giants have said on a number of occasions that they want to sign the Englishman on a permanent deal, but it is understood that they will struggle to agree a fee with United.
According to Gazzetta dello Sport, Smalling is expected to have his current loan spell extended in order to remain with Paulo Fonseca's side for the remainder of the 2019-20 season.
However, the report claims that the former non-league defender could also spend next term with I Giallorossi, providing that the Italian side cover his wages once again.
Smalling's contract at Old Trafford is due to run until the summer of 2022.