Versatile Austria international Alaba was ruled out for several weeks earlier this month, after suffering a partial tear of the medial collateral ligament and damage to the medial meniscus in his right knee during Bayern's UEFA Champions League meeting with Roma.
However, the 22-year-old is confident he can soon return to action having undergone successful surgery.
"The knee's looking good and it's feeling good too," Alaba told Bayern's official website.
"I'd like to be back with the team in time for the training camp in early January."
Bayern face Hoffenheim on Saturday, a club Alaba spent time on loan with in the second half of the 2010-11 season.
While Alaba recognises the progress made by Markus Gisdol's side, who currently sit fifth in the Bundesliga, he is confident Bayern will prove too strong for their opponents.
"It's obviously a shame when you can't face your former friends," said Alaba of Hoffenheim.
"We will win ... but they're in really good shape this season.
"They're playing very well as a team and scoring lots of goals - that's their big plus."