Mbappe, who is out of contract next month, is a long-standing target of UEFA Champions League finalist Madrid, although PSG has also made its desire to keep the 2018 FIFA World Cup winner public, with head coach Mauricio Pochettino declaring on Friday he wants the France international to stay "for many more years".
He has scored 25 league goals and added 17 assists to guide PSG to its 10th Ligue 1 title this term, with his total of 42 league goal contributions the highest of all players in the big five European leagues.
Mbappe was voted Ligue 1 player of the season for a third successive time last week, before declaring at the Union Nationale des Footballeurs Professionnels (UNFP) award ceremony in Paris that he would announce a decision on his future before France's UEFA Nations League fixtures in June.
The player's mother and agent Fayza Lamary has now confirmed reports that Mbappe has agreed similar terms with both PSG and Madrid.
"There are no new sessions in order to negotiate the future of Mbappe after the expiration of his contract with Paris Saint-Germain. These sessions have ended," she said.
"We have an agreement with Real Madrid and another agreement with Paris Saint-Germain, and the negotiations have already ended, now Kylian has to choose.
"The two offers are equal from Real Madrid and Saint-Germain, there are no big differences between them, but we are waiting for Kylian to choose what he wants."
PSG will bring the curtain down on its Ligue 1 season when it hosts Metz on Sunday (AEST), with Mbappe having contributed to seven more league goals than its final-day opponent has scored this season (35).