Laurent Koscielny insists he "feels good" and wants to stay at Arsenal, but has warned the club they must start challenging for trophies or he could seek a transfer.
The 27-year-old France international played a key role as Arsenal ended the season with a 10-match unbeaten run in the Premier League to clinch fourth spot.
His form has apparently caught the eye of Bayern Munich and there have been reports that the European champions are preparing a £15m bid for his services.
Arsenal manager Arsene Wenger has already issued several hands-off warnings but his side have not won any silverware since the 2005 FA Cup and Koscielny is desperate to end that barren run.
"I feel good at Arsenal, if we have ambition to fight against the other teams of course I want to stay here," Koscielny told Eurosport.
"It's hard psychologically. We are constantly pressured because if Arsenal is not in the Champions League it would be a catastrophe.
"It is hard to not win titles year after year. We are competitors, professionals, we want to win.
"I want to add to my list of achievements. If Arsenal cannot allow me that, I'll seek a move elsewhere."