Crosby skated for less than a minute before practice Sunday but did not return when his teammates took the ice. He said he also skated for about a minute when the Penguins had a day off Monday.
Second-line left wing Alex Galchenyuk also could play Thursday but did not practice. He's day to day with a lower-body injury that held him out of the final two preseason games. He could practice Wednesday, Sullivan said.
Forward Bryan Rust, who had been the second-line right wing in recent practices, was placed on long term injured reserve Wednesday with an undisclosed injury, Sullivan said. He left the game Saturday after taking a shot to the hand from Sabres defenseman Colin Miller.
"As far as health, I think it would have been nice to try to keep everybody healthy and get through [training camp]," Crosby said. "That didn't happen. I think you just find a way. As far as everything else is concerned, I think we competed hard and did some good things.
"It's a process. It doesn't happen Game 1. Our mentality, and that kind of thing, I think it's in the right spot going into Game 1."