The Bavarians are in top spot on goal difference from Borussia Dortmund, also on 49 points, but have seen their lead from the winter break evaporate after winning only half of their eight league matches this year.
Dortmund, meanwhile, have racked up a perfect eight-game winning run to close in on Bayern, who are still aiming for a record-extending 11th straight league title.
Dortmund's last Bundesliga title dates back to 2012 under then coach Jurgen Klopp.
"We will have to see what our path will bring this season, but if we couple our quality with the way we played (against PSG) then a lot is possible," Bayern coach Julian Nagelsmann (35) said.
"If we show this hunger then it will be very difficult to beat us. It is about coupling this hunger with passion. If we couple them then we are unbelievably good. If not then we get nervous."
Bayern, who beat star-studded PSG 2-0 for a 3-0 aggregate win over two legs and a spot in the last eight, host Augsburg in their Bavarian derby on Saturday, and a win is necessary if they are to protect their slim lead for another week.
With Union Berlin in third place five points behind on 44, the title looks to be turning into a two-horse race between Bayern and Dortmund in the last third of the season.
Augsburg, with exactly the same league wins as Bayern in 2023, are in 13th place and look on course to avoid relegation.
But with an average of almost two goals conceded per game, the Augsburg defence will be bracing for a turbulent afternoon against Bayern, who have netted an impressive 66 times in their 23 league games.
Dortmund have a far tougher task away at Ruhr valley rivals Schalke 04, especially in the wake of Tuesday's Champions League exit to Chelsea.
Union travel to VfL Wolfsburg while fourth-placed RB Leipzig, who face Manchester City on Tuesday for their Champions League Round of 16 second leg, host Borussia Moenchengladbach.
