Real Madrid was widely expected to sign Mbappe as a free agent after the expiration of his contract.
However, PSG was determined to keep the 23-year-old forward, who has been in sensational form this season, and it now seems to have won that battle.
Earlier this week the pendulum seemed to have swung firmly in Madrid's direction, with reports suggesting talks between Mbappe and PSG's Qatari owner had not swayed the striker, and that he wanted to join Los Blancos.
Mbappe's mother and agent confirmed on Saturday (AEST) that agreements had been reached with both clubs and a decision would be made over the weekend.
On Saturday, multiple publications in France, including L'Equipe and Le Parisien, as well as ESPN, reported the former Monaco striker will be staying put.
No details were put forward as to the length of Mbappe's new contract, though it was suggested the France star could confirm his decision at Parc des Princes after PSG's season-ending match against Metz on Sunday (AEST).
Mbappe is the club's second-highest goalscorer in its history, behind Edinson Cavani, having overtaken Zlatan Ibrahimovic when he netted for the 157th time in a PSG shirt earlier this season.
The news will come as a blow to Madrid, which faces Liverpool in the UEFA Champions League final next week, ironically a match to be held in the French capital.
Los Blancos had also been linked with Borussia Dortmund star Erling Haaland, but he has decided to join Manchester City, and it appears as though Madrid president Florentino Perez will be made to wait for his next Galactico.