The Dutch international has been a standout performer during a difficult season for the Black Cats and the north east club will struggle to keep hold of him should they be relegated to the Championship.
According to Tutto Mercato, Roma want to sign on-loan full-back Lucas Digne on a permanent basis from Paris Saint-Germain this summer but will turn their attentions to landing Van Aanholt if that deal falls through.
The former Chelsea man signed for Sunderland for £1.5m in 2014 and has emerged as a fans’ favourite at the Stadium of Light.
The 25-year-old has made 35 appearances for club and country this season, netting on three occasions.
But the defender is keeping his options open and a move to Italy, with the possibility of Champions League football next term, is likely to be enough to persuade Van Aanholt to sign on the dotted line.