"I can start running in about five days and five days later I can train with the ball," the Germany captain told Bild newspaper on Thursday. "I expect to be back in March."
Schweinsteiger, 31, spent 17 years with Bayern Munich, winning eight Bundesliga titles, the Champions League and a Club World Cup before moving to Old Trafford in July.
Injuries have marred his first campaign at United, raising concerns about his fitness for the European Championship in France in June especially as World Cup winners Germany are brimming with midfield talent with the likes of Ilkay Guendogan and Toni Kroos.
"I have played 27 matches this season despite injuries and suspensions. Obviously some things could have gone better but to claim that is a bit far fetched," said Schweinsteiger of the doubts.
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"A ligament tear takes time but it is healing well and I know my body. Everything will be fine.
"Unless the Euros are suddenly moved to March everything is looking good," added Schweinsteiger.
United bid to overturn a 2-1 deficit from the first leg when they host Denmark's Midtjylland in their return Europa League last-32 tie later on Thursday.
(Reporting by Karolos Grohmann; Editing by Tony Jimenez)
