Beckham's Los Angeles Galaxy contract runs out at the end of December and PSG - top of Ligue 1 after the arrival of new Qatari owners in the summer - have become the favourites to sign the former Manchester United player.
The 36-year-old revealed that he has been courted by "two big European clubs" after helping the Galaxy to the MLS title last weekend.
Former AC Milan manager Leonardo, who coached Beckham during his loan move at the San Siro last year, confirmed PSG were one of those clubs as they look to bring one of football's most high-profile names to the French capital.
"Yes, we've spoken. These situations take time. We'll see if something suits him and suits us," Leonardo was quoted as saying in The Sun.
"I know his history and he doesn't need to tell me his past. He went to Milan and it was the same thing. There is a rapport with him.
"When you talk about Beckham, you're talking about something big. Now his contract is finished, he will decide his future."
PSG's interest in Beckham has been derided in some parts as a publicity stunt as the club's new owners look to cash in on his worldwide appeal.
Leonardo, however, claimed Beckham could provide a key part in their push for a first French title since 1994.
"If Beckham thinks about coming, that's something we should be happy about," Leonardo said.
"I think he can still bring something on the pitch with the person he is and the experience he has.
"If a player like him is thinking about Paris St Germain that's good, and we've opened the door for discussions.
"Everybody's talking about PSG and that pleases me. PSG are on the up, there are 45,000 people in the stadium and everyone's happy."