Qatari investors have ploughed millions of euros into PSG since buying the club in May and the 36-year-old former England captain, whose Los Angeles Galaxy contract ends in the coming weeks, is seen as a key target.
"David Beckham goes beyond the sport. He is an ambassador, he is a brand, he is an example to others," PSG president Nasser al-Khelaifi told L'Equipe.
"But he is also still a very good football player whose age is not a problem."
Beckham inspired Galaxy to Major League Soccer's Western Conference final with a 2-1 win over New York Red Bulls on Thursday.
The former Manchester United, Real Madrid and AC Milan winger has said he is yet to decide on his future and will wait for the MLS season to end. Retirement is not on his mind and he is keen on a spot in Britain's 2012 Olympic team.
"People are saying that I'll go to Paris Saint-Germain because my wife would love Paris but the deciding factor will be about what is best for my family and for me to keep playing - none of my moves have been about Brand Beckham," the ex-England midfielder was quoted as saying in Saturday's Daily Telegraph.
Galaxy team-mate Landon Donovan has said the players are "assuming" Beckham, who has the right to buy an MLS franchise when he retires, will renew his contract with the LA club.
English clubs Queens Park Rangers and Tottenham Hotspur have shown interest in Beckham but he has often said he would find it difficult to play for any other Premier League team than his beloved Manchester United.
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