The centre-back has spent the last nine seasons at Old Trafford, making a total of 281 starts and 42 substitute appearances in all competitions.
However, the Englishman now finds himself behind Harry Maguire and Victor Lindelof in the pecking order, with Phil Jones, Axel Tuanzebe and Marcos Rojo also in reserve.
Given the options available to manager Ole Gunnar Solskjaer, Sky in Italy claim that United have given the green light for Smalling to spend the campaign at Stadio Olimpico.
The report adds that Roma will pay a £2.7m loan fee, while also possessing the option of signing the 29-year-old on a permanent basis next summer.
Smalling has not featured in any of United’s opening three Premier League fixtures this season.