PSG sporting director Leonardo insisted preliminary talks have already taken place and that he has a good rapport with Beckham.
Leonardo — who was Beckham's coach on a loan spell at Milan — said: "Yes, we've spoken. These situations take time. We'll see if something suits him and suits us.
"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.
"If Beckham thinks about coming, that's something we should be happy about.
"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 Saint-Germain that's good, and we've opened the door for discussions.