The Manchester United defender has fallen out of favour at Old Trafford following the summer signing of Harry Maguire.
Smalling has yet to make an appearance for Ole Gunnar Solskjaer's this season.
And with the European transfer window still open until Monday, Roma are poised to complete the signing of the former Fulham centre-back until the end of 2019/20.
The Italian outfit will pay £2.7m to borrow Smalling until next summer, but the deal does not include an option to buy.
The England international, who has won two Premier League titles at Old Trafford, made 34 appearances for United last season but is not currently in Solskjaer's plans.
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