The Spain international has been sidelined since suffering the problem in his country's friendly with England on 13 November.
However, at a sponsor's event with Bayern on Wednesday, the former FC Barcelona midfielder confirmed he is fit again, even if next week's UEFA Champions League group stage closer at Dinamo Zagreb means he may have to wait to step out onto the training pitch with the rest of Pep Guardiola's men.
"I want to get back into training on Monday," the 24-year-old explained. "Unfortunately, the team won't be training in Munich, because they're flying to Zagreb on Tuesday. So, I'll wait until they return, or there is the possibility that I'll travel with them."
The news comes as a further boost to Bayern after Franck Ribery started training again this week after nine months out with an ankle problem, and Mario Götze is also on the road to recovery after suffering an adductor injury while playing for Germany in October.