Manchester United boss Solskjaer is facing a fight to keep Bailly, with Arsenal keen on signing the Ivory Coast international this transfer window.
The centre-back has endured a rocky time at Old Trafford ever since touching down from Villarreal in the summer of 2016.
Manchester United saw the best of Bailly during his first season at the club, with the centre-back helping the club win the EFL Cup and Europa League.
Injuries have prevented him from kicking on, though, with the 24-year-old falling down the pecking order as a result.
Despite his struggles, however, journalist Duncan Castles has claimed that Solskjaer has already told Bailly he wants to keep him.
That’s despite Arsenal trying to secure his signature.
“I know that [Arsenal] have a longstanding interest in Eric Bailly and have approached him to find out if he’d be interested in moving to Arsenal,” he said on The Transfer Window podcast.
“But the question mark in that deal has been: would they have the money to give Manchester United back what they paid to sign him three seasons ago?
“That essentially came down to whether they qualified for the Champions League or not, and when they didn’t, it doesn’t look like they’re gonna have the resources to get Bailly out.
“And Bailly himself has been told that Solskjaer doesn’t want to sell him.”
Bailly missed United’s final few Premier League matches after picking up an injury in April.
But, speaking at the time, the Ivorian vowed to bounce back better than ever.
“I would like to thank everyone for the messages of love and support I have received,” he said.
“It’s tough but one must accept that some injuries are unavoidable.
“It’s true that this season hasn’t smiled down upon me very much, but I will return soon and with more strength next season. God willing.”
Arsenal are keen to sign a centre-back – and so too are United.
Links to Matthijs de Ligt have finally died down, with the Holland international looking likelier to join Juventus.
But United want Harry Maguire, while Issa Diop has also found himself on the Red Devils’ radar.