Smalling, 29, joined United from Fulham in 2010 and extended his contract at Old Trafford to 2022 in December.
“This opportunity for Chris has come up in the last couple of days,” said Solskjaer on Friday.
“We’ve got six fit centre-backs. I couldn’t promise him regular football.”
Roma sold Greece centre-back Konstantinos Manolas to Napoli for £32m this summer.
Smalling made 34 appearances last season but is now on the fringes of the squad, with fellow England defender Harry Maguire – an £80m summer signing – and Sweden international Victor Lindelof established as the first-choice centre-back partnership.
Solskjaer said Marcos Rojo, who has been linked with AC Milan, Marseille and Monaco, is “staying definitely”, along with fellow centre-backs Phil Jones, Eric Bailly and Axel Tuanzebe.
“We’ve got a squad now that’s less in numbers but still big enough and strong enough to have coverage in all positions,” added Solskjaer, who also confirmed Italian right-back Matteo Darmian is likely to be returning to his homeland.
More to follow.