Bayern was dealt a big blow when Germany international Sule tore the anterior cruciate ligament in his left knee during the 2-2 draw with Augsburg on Sunday (AEDT).
The centre-back underwent surgery the following day and has been told by Bayern president Uli Hoeness to forget about returning before Euro 2020.
Sule's absence leaves head coach Niko Kovac with key decisions to make for Tuesday's Champions League date with Olympiacos and the remainder of the season.
World Cup winner Pavard and the versatile Joshua Kimmich are the only fit defenders to have started all eight Bundesliga games this season.
Asked if he is the now considered the leader at the back, Pavard told Sport1: "I don't know, I need to talk to the coach first. We'll see, but I've played a lot of games in a row now.
"I hope I can play against Olympiacos again and take more responsibility.
"In any case, I feel good and hope that continues."
Regardless of seniority, the 23-year-old wants his team-mates to begin delivering stronger performances defensively.
Kovac's men have conceded two goals in each of their past four matches in all competitions.
"We are conceding a lot of goals at the moment," Pavard said.
"We urgently need to improve and again allow fewer goals. I hope we keep Olympiacos to zero, that would do us good."
Bayern, 7-2 winners over Tottenham in their last Champions League outing, are top of Group B with six points from two games.