Fosu-Mensah is out of contract at the end of the season and has held talks with overseas clubs but Solskjaer is unsure whether the Dutchman will leave before the January transfer deadline, when United could obtain a fee.
“I’m not sure if he will stay or if he’s going to take an option now,” Solskjaer said. “He’s not played enough, so of course he’s been allowed to speak to clubs with a view to leaving now in January.
“It’s difficult when you have good players, talented players, and you can’t give them game-time. He’s now at the stage where he needs to go and play again.
“It might be end of January or in the summer where he finds somewhere else, he’s working hard so he’s ready for a move for any club he feels ready for.”
Fosu-Mensah could be involved in United’s FA Cup third round tie at home to Watford on Saturday night as they attempt to recover from their latest semi-final defeat to Manchester City.
United have been eliminated from the Champions League and the Carabao Cup in successive months but could go top of the Premier League next week and are in the Europa League, as well as the FA Cup.
“It’s a competition we always enter to go as far as we possibly can,” Solskjaer said of the FA Cup. “It’s the first round we can join in. We were all disappointed on Wednesday night but we were all ready to go again on Thursday morning.
“We have got to bounce back and there’s still many many game to go. Quarter-finals in 2019, semi-finals in 2020, hopefully we can go one step further this season.
“Then again to get there you have to play so many games and so many good teams so we have to just focus on this on Saturday.”