Roma are looking to thin out the squad this summer, with the aim being to lower the wage bill at the club.
The club could offload a defender and view Smalling as a potential candidate to cash in on, following an injury interrupted last season for the centre-back.
Everton are interested and, according to Italian daily Il Messaggero, they are continuing to make enquiries into Smalling’s situation in Rome and his availability.
The Toffees are without a manager at present, though they are tipped to appoint Rafael Benitez, and director of football Marcel Brands is leading their transfer market work.
Roma have appointed Jose Mourinho as their new manager and the Portuguese is claimed to feel that Smalling is surplus to requirements.
Mourinho also wants to make signings to reshape the squad and offloading Smalling would bring in money and make space on the wage bill.
The former Tottenham Hotspur boss is currently chasing Arsenal midfielder Granit Xhaka.
