Both centre-backs took part in the majority of training on Sunday.
Despite the draw with Mainz, Bayern are still just two wins away from defending their title.
The Bavarians were disappointed after Saturday's 2-2 draw against FSV Mainz.
The Bayern defender had to be subbed off with injury early in Bayern's home match against Mainz...
fcbayern.com presents some facts and stats on the Bundesliga meeting with Mainz.
Hoffenheim, Werder Bremen and hosts Gladbach will also be playing in the tournament.
The FCB netminder will be sidelined for the rest of the season, but does not require surgery.
Philipp Lahm and Xabi Alonso contested their final match in Europe's premier club competition on...
Despite fitness problems, Hummels and co gave everything in Madrid.