Roma will pay an initial €15 million with €5 million in add-ons, according to The Athletic's David Ornstein.
The two clubs now face a race against time to complete the relevant paperwork and finalise the deal before the deadline. The Serie A transfer window shuts four hours earlier than the UK, with 8pm CET being the time to beat for United and Roma to do the deal.
Smalling spent last season on loan at Roma, and made 30 appearances. He helped Roma finish fifth in Serie A, and also was part of the initial stages of their Europa League campaign.
He was not allowed an extension to his loan deal by Manchester United to allow him to compete in the latter stages of last season's Europa League, where Roma and Manchester United were both eventually eliminated by champions Sevilla.
Smalling is expected to go straight into Paulo Fonseca's back three, when the Serie A resumes after the international break. The side from the Italian capital also signed Marash Kumbulla from Hellas Verona to add depth in that centre-back position.
Manchester United could complete signings of attackers
On deadline day, Manchester United have already confirmed the arrival of left-back Alex Telles from Porto, for a reported fee of around £13.5m.
They are also expected to confirm the signing of free agent Edinson Cavani before the window closes.
Their search for a winger is still on-going, with moves for Watford's Ismaila Sarr, Atalanta's Amad Traore and Penarol's Facundo Pellistri all still possible. A deal for 18-year-old Traore may yet roll over to January if it is not complete in time.
The summer-long saga featuring Jadon Sancho appears to have met a futile end. Borussia Dortmund have not budged on their €120m asking price, while Manchester United have spent the whole summer trying to convince them to lower their price.
Reports on deadline day are also stating that Manchester United are in talks with Barcelona over a potential deal with Barcelona for Ousmane Dembele.
However, with no agreement yet, and Manchester United facing a race against the clock, it remains to be seen if that deal can proceed to be finalised before the window slams shut.
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