The Spain international goalkeeper, who has yet to make his competitive Bayern debut, suffered the setback during a friendly in early October.
Reina's absence has left coach Pep Guardiola with Leopold Zingerle as back-up to Manuel Neuer, but the 20-year-old's services have not been required.
Having spent time recovering Reina is now in a position to return to training, and he has set his sights on challenge Neuer for the number one spot at the Allianz Arena.
"I'm really looking forward to playing again," he told the club's official website. "I'm energised by the sense of anticipation.
"I've been working very hard over the last few weeks. I'll be stronger for it when I come back.
"There's quite a few of us [injured] at the moment unfortunately, so it's not easy. But the good thing is that we mutually encourage each other.
"That's very important at a time like this."
Reina completed his jogging and co-ordination drills on Tuesday, and is expected to increase his workload before returning to goalkeeper-specific sessions.
