According to The Sun's Daniel Cutts, the former Sweden international has been working on his core fitness in the gym since his last outing on Boxing Day, but in recent days has furthered his recovery; he is able to run without problems and is expected to begin working with a ball again imminently.
A source at the club told Cutts:
"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."
Ibrahimovic arrived at Old Trafford ahead of last season and enjoyed a superb campaign, contributing 28 goals and 10 assists before it was cut short when he suffered a serious knee injury in April.
The 36-year-old returned to action in November and made seven appearances for United before returning to the sidelines.
Football writer Liam Canning cast doubt on his future at the club:
Ibrahimovic has spent much of his storied career defying expectations, but it's unlikely he'll remain with United beyond the end of the season and unlikely he'll have any suitors among Europe's top clubs.
It seems his return before Christmas was premature, but if he can return to full fitness, he could still be an asset for the remainder of the campaign.
He may have to accept a back-up role, though. Despite his quality, United often lack fluidity when he's on the pitch. With Romelu Lukaku now at the club, the Red Devils have a more mobile option up front, one they hope can lead the line for years to come.
Nevertheless, as an option from the bench or alternative to Lukaku should he pick up an injury or be in need of rest, Ibrahimovic could still have a big say in the rest of United's season.