"I'm going to say what I've said all along. I'd prefer to keep him," Rutherford said. "We play a lot of games in March. You don't know when players are going to get hurt. He's handled the situation very well.
"I'm going to have some communication with him in between now and the [deadline] and see exactly where he sits and how he feels. That will play a part in the final decision. But I'm not going to get too far ahead of myself because he very well could be a part of our team going down the stretch."
Trade talks regarding Fleury and Murray began during the offseason after Murray won 15 of 21 playoff starts to help the Penguins win the Stanley Cup. Murray, 22, replaced Fleury, 32, as the starting goalie after Fleury sustained his second concussion in four months against the Nashville Predators on March 31.
Before that, Fleury was enjoying possibly the best regular season of his NHL career. He was 35-17-6 with a career-low 2.29 goals-against average and .921 save percentage in 58 starts.
Fleury started once in the 2016 playoffs but allowed 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 the final eight games of the playoffs, averaging 2.86 goals against during that stretch.
After initially splitting time with Murray earlier this season, Fleury has become Pittsburgh's de facto backup. He is 2-0-1 in three starts since Jan. 14 and 15-7-5 with a 3.16 GAA and .906 save percentage this season.