It's believed the Los Angeles Kings and Nashville Predators were among the teams interested in Gagner earlier this season, and while a deal was reportedly close with the Kings, it ultimately fell through.
Gagner was limited to 67 games this season due to ankle issues and a broken jaw. He collected 10 goals and 27 assists for 37 points.
"It's been tough (with the injuries) but I need to take responsibility for the way the year has gone as well," Gagner told the Edmonton Journal. "I know it's not good enough -- especially with my role on the team. If we're going to take any steps forward, I need to do that as well."
Oilers GM Craig MacTavish is expected to be fairly active this off-season and while there are no guarantees Gagner gets dealt, it remains a possibility.