The Italian outfit had Smalling on loan last season, and he impressed.
Goal and other sources are confirming Roma's intention to launch another offer for the player.
They have currently bid €12 million for the Englishman, who is not first choice at United.
The 30-year-old is willing to take a pay-cut to secure the move, as he enjoyed his time in Rome.
It is unclear if United would accept the €12 million offer, as they are looking to raise money through sales to fund their own summer movies.