Fleury, who was not available Thursday, signed a four-year, $23 million contract on Nov. 5, 2014. At the time, he was set to become an unrestricted free agent on July 1, 2015.
After sustaining his second concussion of the season on March 31, Fleury started one game in the Stanley Cup Playoffs, allowing four goals on 25 shots in a 4-3 overtime loss to the Tampa Bay Lightning in Game 5 of the Eastern Conference Final. Murray started each of Pittsburgh's remaining eight playoff games and helped the Penguins win the Cup in a six-game series against the San Jose Sharks.
Murray, 22, won 15 of 21 playoff starts with a 2.08 goals-against average and .923 save percentage. He also impressed in the regular season, when he went 9-2-1 with a 2.00 goals-against average and .930 save percentage.
The Penguins complimented Fleury's selflessness through the playoff run. Rutherford said he is not concerned with how Fleury, who he called "as good a pro as you can find in any sport," would handle a goalie controversy moving into next season because he has seen his demeanor the past two months. He also said the Penguins need to be realistic about the situation they face.
"We have two very good starting goalies," Rutherford said. "One who's starting his career and one that's had a great career and has many, many more years left in him. Is it really possible that those two guys are going to play 40 games each? Is it possible one could play 50 and 30? I'm going to say the obvious. It's a great situation because we have good goalies. But it could be a tough situation going forward."
Murray said he would like Fleury back. He also said he has no expectations regarding keeping his starting position next season.
"I just take things as they come and with hockey, I just play and compete whenever I'm out there," Murray said. "I don't know where I'd be if [Fleury] wasn't around here. He's guided me through this and given me advice along the way. Obviously, it was my first time going through something like this and he's done it before, so he's been a huge source of advice for me and like I said, he's helped me stay calm under pressure … He's a huge mentor for me. I hope he says the same, that we have a friendship."
Fleury was named Penguins MVP on April 10 after going 35-17-6 with a 2.29 goals-against average and .921 save percentage.