The 24-year-old World Cup winner was a regular in the Bayern line up before rupturing knee ligaments in September.
German press reported on Monday Colisso was now running and back in training again.
"It seems that we will witness the return of Tolisso in March, which is earlier than expected," Bayern coach Niko Kovac said at their Qatar training base.
After a poor start to the season Bayern currently are second place in the Bundesliga behind Dortmund.
"We are only six points behind and we must try to catch-up as fast as we can. We're the hunters. We want to increase the pressure on Dortmund and pick up where we left off when we get back," Kovac told the club's website.
Bayern have won every Bundesliga championship since 2013 and won all of their five league games in December to put some pressure on their rivals.
Kovac had further good news from the Bavarians' injury list.
"Serge Gnabry and James Rodriguez are back with the team. Mats Hummels is doing better. We'll have to take each day as it comes with Arjen Robben," he said of his players who were doing rigorous work outs at their Middle East training base.