Sullivan said he and general manager Jim Rutherford would discuss how Pittsburgh would handle its goaltender situation without Murray.
Backup Casey DeSmith is expected to start against the Vegas Golden Knights at PPG Paints Arena on Thursday (7 p.m. ET; ATTSN-PT, ATTSN-RM, NHL.TV). Tristan Jarry, who competed for the backup position during training camp, could be recalled from Wilkes-Barre/Scranton of the American Hockey League.
"They're good goalies," Sullivan said. "We believe in these guys. They're young guys, but their body of work last year was very strong. They won games for us. We believe these guys can make the timely saves for us to help us win.
"So it's at times like these where we have to rely on our depth and we believe in the group that we have. I think both Casey and Tristan have shown that they're NHL-caliber goalies."
As a rookie last season, DeSmith was 6-4-1 with a 2.40 goals-against average and .921 save percentage in 14 games (11 starts) with the Penguins. Jarry, who was also a rookie, was 14-6-2 with a 2.77 GAA and .908 save percentage in 26 games (23 starts).
"I've been having really good practices lately," DeSmith said. "I felt good out there. I've got all the new gear broken in, so that always feels good. The beginning of the season is always rough, at least for me. So yeah, everything's coming together for me.
"Obviously, you never like seeing [Murray] go down, that's for sure. But I have a good opportunity with a really good team coming in Thursday."
Kris Letang said the Penguins defensemen would not play any differently in front of DeSmith or Jarry than they would Murray. He also said losing Murray for an extended period of time wouldn't be ideal, but he trusts DeSmith.
"It [stinks]," Letang said. "It's part of the game. We lose a big piece with Matt. So somebody has to rise to the occasion. Casey's been waiting for the chance. ... I've always thought he was pretty solid. He's an unorthodox kind of goalie, so it's hard to find holes. He's good at reading where your shot is going to go. So I like him a lot as a goalie."