"It's time to move on," Sullivan told ESPN.com Tuesday. "It'll be interesting to see what happens once the market opens."
Sullivan, who will be an unrestricted free agent Friday, turns 37 on July 6. He had 22 points (10 goals, 12 assists) in 44 games last season, was hindered by groin issues, and had surgery in March.
He returned for the end of the regular season and was in nine postseason games before he suffered a knee injury against the Vancouver Canucks.
"The injuries I had this year -- sports hernia and an MCL -- they're injuries a 25-year-old could have easily had as well," said Sullivan, who added that he is "100 percent" healthy now. "They're not chronic injuries, they're just part of the game. Those have healed very well."
He missed close to two calendar years with a career-threatening back injury, but came back during the 2008-09 season and hasn't had a back issue since.
Sullivan, who was traded to the Predators by the Chicago Blackhawks in February 2004, finishes his tenure in Nashville with 263 points in 317 games.
"It's unfortunate that every good thing comes to an end," Predators general manager David Poile told The (Nashville) Tennessean. "Steve will go down in our history as one of our best and most popular players."
Pierre LeBrun covers the NHL for ESPN.com