The Swedish forward has not featured since a 2-2 draw against Burnley at Old Trafford on Boxing Day.
Ibrahimovic suffered a setback in his recovery from a serious knee injury sustained in the Europa League last season.
But it appears that he is now on the verge of a return before United travel to Spain for the first-leg of their Champions League tie.
The 36-year-old has been restricted to just one start in the Premier League this season, largely due to injury problems.
Ibrahimovic is expected to remain behind Romelu Lukaku in the pecking order on his return, and some have expressed doubts over his contribution this season.
Manager Jose Mourinho, though, insisted last year that the former Barcelona and PSG man still has a part to play.
“I see Zlatan as important for the team,” he said. “I just say that my squad is better for sure, he is one more option, he is one more striker, he is one more experienced player, he is one more player that can play nine or ten, that can play double strikers or no, there are lots of matches to play.”
Midfielder Paul Pogba has also returned to training after missing Saturday's FA Cup win over Huddersfield with illness.
He was joined by Ander Herrera, Marcus Rashford and Antonio Valencia, all of whom were absent at the weekend.