Manchester United defender Chris Smalling is on his way to Italy to finalise a loan move to Roma.
Harry Maguire's record-breaking acquisition this summer increased the number of senior centre-backs at Old Trafford to seven, although Eric Bailly is currently laid low by injury.
There has been speculation about the future of Marcos Rojo, Phil Jones and Smalling, with the latter set to head for pastures new for the remainder of the season.
The 29-year-old, who signed a new deal until 2022 in December, is close to joining Roma on loan, with Solskjaer confirming he is en route to Italy to finalise the move.
"It's just come up the last couple of days, this opportunity for Chris," Solskjaer said.
"Of course we sat down yesterday and discussed it. At the moment we've got six fit centre-backs. I couldn't promise Chris regular football.
"He's on the plane over now. I think he'll enjoy the experience over there.
"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."
Romelu Lukaku and Alexis Sanchez have already left United for Italy this summer by joining Inter Milan, while Matteo Darmian also looks set for a move to Serie A.
However, Rojo, subject of an enquiry from Everton earlier in the month, will be staying at Old Trafford.
"I can see maybe Matteo (leaving)," Solskjaer said.
"There has been some interest in Matteo over in Italy, wanting to go back home.
"Marcos - he's staying, definitely. We've got a squad now that's less in numbers but still big enough and strong enough to have coverage in all positions."