Saying he was "shocked and disappointed," Murray said he would try to accommodate Heatley's trade demand, ideally before next week's NHL draft.
"I have had some conversations with several teams," Murray told reporters. "I don't really have a timetable but I have encouraged anybody that is really interested to try to make the contact before the draft and we will get something done by that time I hope."
Heatley, 28, has four seasons remaining on a six-year, $45 million contract that he signed in 2007. He might be difficult to move as he'll cost $7.5 million against a team's salary cap next season.
Heatley had 39 goals and 33 assists for Ottawa last season. He has scored 50 goals in a season twice in his career.
"It's hard to give up 50 goals," Murray told reporters. "He didn't get it last year -- a lot of people underachieved -- but Dany Heatley is that caliber of goal scorer. To be better than that is going to be difficult, there's no question."
Murray said that coach Cory Clouston was "devastated" to learn of Heatley's trade demand but said that the coach's deteriorating relationship with Heatley isn't the only reason the winger wants out of Ottawa.
"That's not totally true," Murray said. "It is part of the reason."