The 33-year-old has been in Italy since 2019, initially on loan from Manchester United and then completing the transfer for a total €18m.
He has been a regular in the defence under Jose Mourinho and his current deal is due to expire in June 2023.
According to Radio Radio, if Roma do not manage to agree a new contract with Smalling, then the defender could stay on in Italy with a free transfer to Inter.
Nerazzurri coach Simone Inzaghi is said to be an admirer of Smalling and wants him to fulfil the same role that Francesco Acerbi is this season, bringing experience to the side.
Smalling also has an eye for goal, finding the net three times in 15 Serie A appearances so far this term, and Roma do hope to keep hold of him for another year at least.