The 30-year-old English midfielder is scheduled to return to his parent club Queens Park Rangers at the end of the season when his loan deal with OM runs out.
"I want to stay, but unfortunately it's not only up to me," he told TF1. "I belong to another club.
"I had a discussion with the OM board last week and I could well extend my stay here. Everyone knows just how much I want to stay here and be part of this club in the future. If I had it my way, I will finish my career at OM."
Barton has two years left on his current contract with QPR.