There was a deadline of 31 July for Mbappe, 24, to tell PSG if he was going to renew until 2025.
After months of talks, he has sent the club a letter saying he will not.
UFABET PSG's record goalscorer would be free to leave for nothing at the end of next season and the move could be a negotiating tactic.
However, as the French champions try to readjust their team-building policy after years of buying star players with no obvious coherent strategy, PSG have resolved not to let Mbappe go for nothing, with the club irritated that the letter was leaked in the media before they saw it.
It means that unless they get assurances about the 2018 World Cup winner's future intentions, they will sell him in a move that would put Europe's leading clubs on alert.
Real Madrid are long time admirers of the Frenchman and he rejected a move to the Bernabeu to stay at PSG last year.
