Leonardo is among those hoping an extension can be put in place, but concedes that any decision on his future will be left in former Manchester United star Beckham's hands.
"He was the first person I called when I arrived at PSG," the Brazilian told TF1.
"He's a leader in the dressing room, it's a privilege to have him with us. We are trying to continue with him, but at 38 (Beckham turns 38 next month) it's up to him to decide.
"He has the desire to play, but there's all the rest, his life. PSG's doors are open, if he wants to stay on, he's going to stay on."