The 30-year-old was deemed surplus to requirements by Ole Gunnar Solskjaer last summer following the world record transfer of Harry Maguire, who moved to Old Trafford from Leicester in an £80million deal.
Smalling, who has not been present at Carrington this week, subsequently moved to Roma on loan and enjoyed a reputation enhancing season in Serie A, making 37 appearances in all competitions and helping his adopted club qualify for the Europa League.
United value the player bought from Fulham by Sir Alex Ferguson a decade ago at, according to the Daily Telegraph, between £15m and £20m and Smalling, who has made over 300 appearances for the Red Devils, is hopeful his future can be resolved imminently.
Solskjaer is keen to sign another centre-half, preferably a left-footed one, to provide competition for both Maguire and Victor Lindelof. United harboured an interest in Bournemouth’s Nathan Ake, but the Netherland’s international jumped at the chance to join Pep Guardiola’s Manchester City side instead.
United have thus far been relatively inactive during the transfer window with Ajax’s Donny van de Beek the only major addition.
Speaking about his new midfield signing earlier this week, Solskjaer said: ‘When we signed Bruno Fernandes, we knew we needed that kind of player, now we’ve signed Donny and he’s a type of player I felt we needed in the squad. He’s the type of person that will fit the culture, fit the team and will improve us next season and for years to come.
‘Our forwards scored quite a few goals last season, Bruno came in and scored goals but we need goals throughout the squad because we didn’t score enough to be challenging at the top.
‘He’ll add his creativity, his reading of the game, his understanding of the game. He can see space and arrive at the right time. ‘The timing of his movement is fantastic.’