The goalie was sidelined for nine games with a lower-body injury. Goalie Tristan Jarry was reassigned to Wilkes-Barre/Scranton of the American Hockey League.
Murray was a full participant during practice Tuesday.
"It feels good to practice]," Murray said. "You kind of take it for granted how much fun it is to be out there with the team."
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The Penguins (13-10-6) were 5-2-2 in the games Murray was injured, and 6-2-3 since his last start Nov. 17.
"We'd like to get him involved as soon as we can," Sullivan said Tuesday. "We're playing a lot of games here. So we need two goalies to participate, to help us. And Matt's obviously an important part of this team. So we'd like to get him involved as soon as we can. When we know he's at his best, he's our No. 1 goalie.
"We're encouraged he's as close as he is. We'll take each day as it comes, but we'll try to make those decisions when he's available to us."
Murray is 4-5-1 with a 4.08 goals-against average and .877 save percentage this season. The Penguins have lost each of his past six starts since he won Oct. 25, when he made 38 saves in a 9-1 victory against the Calgary Flames.
When Murray's injury was made public, Sullivan said it had been lingering throughout the previous weeks. On Tuesday, Murray said the injury did not cause his poor performance.
"I'm not going to use it as an excuse," the 24-year-old said. "Yeah, I was sore, but it was nothing to come out of play with. I was playing on it for a few weeks and it was fine. Just tweaked it the one day there. So it didn't really hinder many different parts of my game either. It's a pretty specific injury."
DeSmith is 9-4-4 with a 2.34 GAA and .925 save percentage in 20 games (16 starts) during his second NHL season. He has won six of his past eight games, including 25 saves in a 2-1 shootout win against the New York Islanders on Monday.
DeSmith started with Murray available Nov. 19 (a 5-4 overtime loss to the Buffalo Sabres) and Nov. 21 (a 5-1 win against the Dallas Stars). Though Sullivan routinely called Murray the Penguins' No. 1 goalie, the coach said he would start the goalie he felt gave them the best chance to win.
"You want to be in there as much as you can, but at the end of the day, that's not up to me," Murray said. "So all I can do is just compete in practices and in games. Do my best in the weight room to get stronger. Do every little thing that I can to be prepared. When my name's called, I'm ready to go. When it's not, I'm practicing as hard as I can."
