"I'm staying in shape, but I'm not going to just jump into any situation," the 36-year-old forward told The Athletic for a story published Monday. "I do it because I love it, and because I know I still can play, but it's going to have to be the right fit."
Pominville played the past two seasons with the Buffalo Sabres. He had 31 points (16 goals, 15 assists) in 73 games last season after he had 34 (16 goals, 18 assists) in 82 games in 2017-18.
Pominville said a return to the Sabres would be "ideal," and his agent, Normand Dupont, said they would "listen carefully" to an offer from the Montreal Canadiens. Pominville is a native of Repentigny, Quebec, less than an hour's drive from Bell Centre.
"When you don't have kids, or when the kids are really young, it's easy to just pack your suitcases -- younger kids will adjust," said Pominville, who has a 9-year-old son and an 8-year-old daughter. "But at the age my kids are at, it's a little tougher."
The market for free agent forwards who are 35 and older has been slow this offseason. Justin Williams, 37, Patrick Marleau, 39, and Joe Thornton, 40, are among those who remain unsigned.
"The League is getting younger and the 35-and-older players have become something of a secondary wave of free agents," Dupont said. "Nobody's panicking. … I'm not worried at all for Jason, it's just going to come together a little bit later."
Pominville, who was selected by Buffalo in the second round (No. 55) of the 2001 NHL Draft, has 727 points (293 goals, 434 assists) and a plus-44 rating in 1,060 games with the Sabres and Minnesota Wild.