Smalling spent last season on loan at Roma, and both the club and player are keen to make the move permanent.
Italian outlet TeleRadioStereo reports that a deal between the two clubs is getting close.
And the Serie A have also asked about the availability of midfielder Fred.
The Brazilian is happy at Old Trafford, but the signing of Donny van de Beek pushes him further down the pecking order.
Fred worked with Roma boss Paulo Fonseca at Shakhtar Donetsk.