"I like Leonardo a lot, he is a great manager," the former England skipper and Manchester United star told Canal+ television on Sunday.
"I'm honoured to know that he wants me to join PSG but I am a LA Galaxy player. It's exciting, great things are happening in France. Leonardo has arrived, there's a lot of money," added the 36-year-old.
"I will wait until the end of the season and see how I feel and then I will decide. My children have been going to school in Los Angeles for the last five years. At their age, they need stability."
The season in the United States ends in November and Beckham will then be a free agent.
Leonardo told the BBC in September that he had been impressed by Beckham when he was loaned to AC Milan by LA Galaxy in the 2009-2010 season.
"I coached him at AC Milan and we created a good relationship," the former Brazil international said.
"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.
Beckham flattered by PSG courtship
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