Crosby, who had core muscle surgery Nov. 14 and has missed 27 games, is with the Penguins on a three-game road trip that continued with a 4-3 overtime win at the Colorado Avalanche on Friday and ends at the Arizona Coyotes on Sunday.
"Sid's going through a rehab process, and with the nature of this injury, it's an evolving process," Sullivan told the Penguins website Thursday. "Part of that process is introducing him to the team environment. We'll see how he responds and the medical staff makes decisions accordingly."
Crosby skated Tuesday and Wednesday in Las Vegas but did not play when Pittsburgh defeated the Vegas Golden Knights 4-3 on Tuesday. He took a scheduled day off Thursday in Colorado and was expected to skate Friday. Sullivan said the Penguins remain hopeful Crosby will take part in a full practice during the road trip.
"I think I've been progressing each week," Crosby said Jan. 3. "I'm happy about that. Obviously, I'd love to be out there right now, but it's just something that when it's time, I'll be out there."
The Pittsburgh Post-Gazette reported Thursday that Crosby has not been cleared to practice without contact restrictions.
"That's a big step," Crosby said. "Once you're cleared for contact, you see how things respond from there. But I'm not ready for that yet. Until then, I think I'll probably flip-flop between doing my own stuff and skating with the injured guys, and then going with the team depending on the practice."
The Penguins are 17-6-4 without Crosby, their captain. He had 17 points (five goals, 12 assists) in 17 games this season, his 15th in the NHL.
"He's had some really strong days," Sullivan said. "You can see him getting stronger with each day that he's out there. I think just his presence around the team, everyone looks up to him. He has a great presence. He's a great teammate. He's close friends with these guys, so for him to be around the team like this is terrific for all of us."
Starting Sunday, Pittsburgh plays six games in 10 days, followed by the NHL All-Star break.
"That's part of the challenge," Sullivan told the Post-Gazette. "It's one of those things that's really out of our control. ... The challenge for the guys that are in the rehab process and [with] reintroducing them into the team environment is trying to get them into team practices and get them the workload that they need."
