Please Wait . . .
The right-back, who can also play centre-back, signed for United from Ajax in 2014 and would prefer a move back to his former club, however, it is understood a move to Leverkusen is looking more likely.
Fosu-Mensah was handed his first-team debut by Louis van Gaal in 2016 but, after loan spells at Crystal Palace and Fulham, he has struggled to push his way into the United first team and Solskjaer confirmed last week that he would be able to leave having played just 108 minutes this season.
"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 the 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."
It is set to be a relatively quiet transfer window for United, with the club only looking to move to bring players in if long-term targets become available.
Argentine duo Sergio Romero and Marcos Rojo could be joining Fosu-Mensah on the departures list with Solskjaer confirming the club would not be extending their current deals.
Both are out of contract in the summer so, if they want to recoup a fee for the goalkeeper and centre-back, United would have to agree deals for the pair during the current window.
Solskjaer gave an update on potential transfers on Monday afternoon when he confirmed there could be a couple of exits.
“I think the signings we made in the summer strengthened squad really well, good signings and good characters and good players," said Solskjaer. "January is always difficult. If something comes up that is a long-term target anyway that is another scenario.