Murray, speaking after the NHL general managers meeting, said he will try to accommodate the request from the 30-year-old center.
"I don't want to trade the guy, really, and I know I won't get the value, in all likelihood, that I should get for him," Murray said. "But I think that Jason feels maybe there's a change that he would like to have happen, and if that's the case we'll try to do what we can."
Murray said getting at least one established NHL player in return would be important in any trade involving Spezza.
Spezza, who was named Senators captain prior to last season, replacing Daniel Alfredsson, has spent his 11-season NHL career with the Senators. He has 687 points in 686 games, including 66 in 75 games this season, when Ottawa failed to make the Stanley Cup Playoffs.
"It'll probably be another few weeks, at least, before anything comes down that might be a worthwhile trade [to talk] about," Murray said.
Taken by the Senators with the second pick of the 2001 NHL Draft, Spezza is second on their all-time list in goals (252) and points (687). He's scored at least 30 goals in a season four times.
He has 52 points in 56 Stanley Cup Playoff games, including seven goals and 22 assists in 20 games to help the Senators reach the 2007 Stanley Cup Final.