Leonardo made the announcement as he unveiled Carlo Ancelotti, who managed Beckham at AC Milan, as PSG's new coach.
Media reports have long said the 36-year-old midfielder was heading to the big spending Qatari-owned club after his five-year deal with Los Angeles Galaxy ran out.
"We have never said it was done," Leonardo told reporters.
"We have a good relationship but I don't know what he is going to do. There is always the question of his personal life. He is in Los Angeles," added the Brazilian, who also coached Beckham in the player's second spell at Milan.
"Nothing is signed."
Tottenham Hotspur and Queen's Park Rangers have both expressed interest in England's most capped outfield player but the former Manchester United winger has said he would find it difficult playing for another Premier League side given his attachment to the Old Trafford club.
His wife Victoria's fashion work led to speculation Paris would suit her well but their children are happy in school in California.
