The defender was heavily linked with a January exit, with Arsenal and PSG making approaches for the 24-year-old.
Bailly has struggled to get game time under the interim Manchester United boss, with the Ivory Coast international starting just two Premier League games.
However, The Sun say Solskjaer has held talks with Bailly to give the defender assurances over his future.
Solskjaer told Bailly he’s in his plans – and he could start alongside Victor Lindelof against PSG in the Champions League on Tuesday night.
Bailly returned to the United starting XI on Sunday afternoon in the Red Devils’ 1-0 win at Leicester.
Speaking after the win, which sent United up to fifth in the Premier League, Solskjaer hailed his defence.
“They fought for their three points today. I think we deserved it in that respect,” Solskjaer said.
“In the second half when we could have controlled it more, we could have slowed it down.
“But we defended really well. Eric and Victor were fantastic and David [De Gea] again of course.
“If you have the foundation of a clean sheet you’ll always be in with a chance to win a game and we’ve got a keeper that saves us, we’ve got a back four that sacrifices everything in the box, a couple of midfielders who made a couple of great blocks.
“That was absolutely amazing to watch and the attitude has been spot on ever since I came.”
Solskjaer was vocal on United’s plans with Bailly in the January transfer window, insisting it wasn’t surprising the defender was in demand.
United are back in action on Saturday afternoon against Fulham in the Premier League.
A win could send the Red Devils into the top four, ahead of Chelsea.
Solskjaer’s men will then turn their attention to the Champions League, where United face PSG.