Smalling spent last season on loan with the Serie A outfit and impressed enough for Roma to try to make the deal permanent at the end of the campaign.
The 30-year-old is keen to make the move permanent too, but the two clubs have so far been unable to agree a fee.
Manchester United are thought to be holding out for £20m, which is some way higher than Roma have offered so far.
The Daily Mail reports that the capital club are considering pulling out of talks due to United's refusal to lower their asking price, and instead will focus on other targets.
Marash Kumbulla, who has previously been linked with United in addition to Arsenal and Tottenham Hotspur, is understood to be on the verge of joining Roma from Hellas Verona.
Smalling made 30 appearances for Paulo Fonseca's side last season.