The Ivory Coast centre-back suffered an injury in pre-season, which ruled him out for the start of the season.
But The Sun reports that Bailly is working hard to get back to full fitness.
And it is possible he could stay at the club and extend his contract, per the same source.
An Old Trafford source said to the paper: "The club want Eric to stay and are looking for talks about an extension.
"We don't want to lose him on a free transfer next summer. It's just down to both parties agreeing to everything.
"His injury record isn't a major concern for us. We just think he has been unlucky with everyone over the last few years.
"Ole is a fan of the player and we're going to convince him to stay, at least that is the plan at present."