Chris Smalling has not been named in the matchday squad yet this season
The Premier League club have reportedly agreed a season-long deal with Roma paying a fee of £2.7m.
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."
"It's a big club, a good league. There's not many English players who have had the chance to play in Italy and I'm sure he'll come back stronger and better for it."
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.
Smalling is the fifth high-profile departure from United this summer, with Romelu Lukaku and Alexis Sanchez going to Inter Milan, and Antonio Valencia and Ander Herrera leaving after their contracts expired.
'He needed to go'
Chile forward Sanchez arrived from Arsenal in a swap deal involving Henrikh Mkhitaryan in January 2018, but the 30-year-old has managed five goals in 45 games during a miserable spell.
United are believed to be subsidising his near £400,000-a-week wages during his
season-long loan deal, after Inter spent £74m on Lukaku.
"Alexis needed to go," said Solskjaer. "He has been here for 18 months and it's not really worked out for him.
"For him as well, to restart and get himself playing regularly, getting himself scoring goals, that loan will only benefit everyone in the end.
"We're going to watch every weekend now to see Romelu and Alexis playing together. We had a decision to make and I'm trusting Anthony Martial, Marcus Rashford and Mason Greenwood to be our centre-forwards."
After making his first start in the last Premier League game of last season, 17-year-old Greenwood has come off the bench in all three of United's league games this term.