Beckham, 36, made a surprise switch to LA Galaxy in Major League Soccer in 2007.
But the former Manchester United and Real Madrid star was unable to trigger the hoped-for explosion of interest in football in the United States and quickly became a bit-part player with England as well.
Leonardo said however he had been impressed by the midfielder when he was loaned to AC Milan by LA Galaxy.
"I coached him at AC Milan and we created a good relationship," the former Brazil international told BBC Sport.
"He is more than a football player, but when you see him every day he trains and plays like a kid.
"He is someone that I really appreciate and admire so much - his values and everything he has done in football."
Asked whether the Qatari-owned club would consider signing Beckham, Leonardo said: "The door is open. He is more than a football player - he's a brand, a pop star. I would always consider him.
"He respects the rules, listens to you and wants the best for the team. That's why for me he is a big example. I worked with him and that's why I talk about his name."
PSG went on a recruitment drive after their takeover by Qatar Sports Investments (QSI) during the summer, spending a French record 80 million euros on players including Argentine star Javier Pastore.
The Paris-based club last won the French league title in 1994, finishing fourth last season. The are currently fourth in Ligue 1, two points behind leaders Montpellier.
Beckham's LA Galaxy contract expires at the end of the Major League Soccer season.