The Ligue 1 leaders snapped Beckham up on a short-term deal in January, with an initial agreement due to run until the end of the season.
The former England international has impressed on his return to Europe from the American MLS and high-ranking coaches and officials at Parc des Princes have called for him to stay on.
Leonardo is among those hoping an extension can be put in place, but concedes that any decision on his future will be left in 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."
Meanwhile, Leonardo has also been discussing his own future, and has revealed that he would welcome the opportunity to manage in the Premier League at some stage in his career.
The former AC and Inter Milan boss said: "As for me, I want to build something that works when I'm gone. I don't know, normally, yes (I will stay), but in my life things are happening which I wasn't expecting.
"I didn't want to become a manager, but it happened, perhaps if one day there was a managerial job in England...but at the moment there's nothing.
"That sounds like a job application but it's not meant like that. I'm really happy here. And I've learned not to promise anything."