The 31-year-old midfielder will see the 18-month deal he signed upon his arrival at Loftus Road in January 2013 expire at the end of the season.
QPR took a gamble on his services following a string of injuries and were unable to cement a Premier League standing after landing the 21-cap England international.
Jenas has, however, enjoyed his time working under Harry Redknapp, with consistency slowing returning to his game.
He is now looking to prove to the QPR coaching staff over the final weeks of the campaign that he is deserving of a new contract.
Jenas said in the Fulham Chronicle: "Would I like to stay? Yeah, definitely.
"QPR took a chance on me when I ruptured my Achilles, and we'll hopefully talk at the end of the season about a new contract.
"There's a few of us in the same situation, and we're fighting tooth and nail to get the club back in the Premier League.
"On a personal level I've been happy with my performances, but I came at a tough time when we were bottom of the league. It's been a weird topsy-turvy experience, but I've enjoyed it."