The Swedish legend has been sidelined with a knee problem since United's Boxing Day draw at home to Burnley.
An Old Trafford source told The Sun: “Zlatan is making good progress and he could be back by the end of February.
“He has not been comfortable with his core fitness levels and wants to make sure he can finish the campaign.
“The last few days have been good for him. He's running at about 85 per cent with no issues.
“He'll continue ball work soon as well. It's a clear sign he'll be able to join his team-mates on the pitch in the near future."