The German midfielder has been sidelined since the 1-0 win over Sheffield United in the FA Cup on January 9 with a knee ligament injury.
There had been suggestions of late that Schweinsteiger could miss the remainder of the season, as well as facing a race against time to be fit for this summer's European Championships.
However, having undergone extensive rehabilitation with United's medical staff and back in his homeland, the 31-year-old is confident that he will be able to resume his playing duties soon.
"I'm on a very good path. A ligament tear needs time, but everything is healing perfectly. Unless Euro 2016 is moved to early March, then it looks very good," he told Bild.
"Injuries are sadly part of the business. It can happen at any time, also in a season before a big tournament. If it has to happen to me, the timing at least could have been worse. I know my body, everything will be fine.
"I can start running again in about five days, and five days later I should back on the ball. The medical team in Manchester, as well as Hans-Wilhem Muller-Wohlfahrt, are pleased. I think I will be back in March."
Schweinsteiger has made 27 appearances in all competitions for United following his summer switch from Bayern Munich.