The 28-year-old has missed his side's last two matches with the groin problem that he picked up while representing France during the recent international break.
Man United stated that the World Cup winner would be "out for a few weeks" earlier this month, but Solskjaer has said that the centre-back is "working hard" and is already back on the training field.
"He's working hard. As I said, it's hard to put a time limit on players that you don't really know, but he's been on the grass and who knows?" Varane told MUTV.
The former Real Madrid defender has made seven appearances for the 20-time English champions since arriving at the club during the summer transfer window.
Man United have conceded six goals in their last two matches without Varane, and the Red Devils will be looking to return to winning ways in the Premier League against Liverpool on Sunday afternoon. body check tags ::