The reigning champions are in contention for a treble after qualifying for the Champions League knockout stages and lying second on goal difference to Hoffenheim in the Bundesliga.
But Stuttgart have yet to lose in Germany under new coach Markus Babbel and drew with Bayern 2-2 in the final league match before the winter break.
Stuttgart have been boosted by the recovery from injury of key players, including Serdar Tasci, Yildiray Basturk, Cacau and Ciprian Marica.
Babbel, a former team mate of Bayern coach Jurgen Klinsmann, took over from Armin Veh in late November. Despite lacking a German soccer federation top flight coaching licence he has been provisionally allowed to coach until the end of the season.
After a shaky start to the season Bayern have improved considerably and the addition of striker Landon Donovan, on loan from the Los Angeles Galaxy, has so far proved a success with the striker netting several times in friendlies.
"If we play as good as we can we will win this tie," Bayern defender Philipp Lahm told Bild newspaper on Monday. "We can beat any opponent on a national level. Only we can stop ourselves in league and Cup competitions."
Other all-Bundesliga last 16 clashes see Borussia Dortmund take on Werder Bremen while Cottbus travel to Bayer Leverkusen.
