"Am I sure to stay at PSG? Yes, I'm committed to the project," Mbappe told Canal+ following Sunday's 3-1 victory over Monaco. "Good for Real that they have Zizou, but I will watch the matches as an admirer."
Mbappe, 20, is one of several players associated with a switch to the Spanish capital as part of a potential offseason squad overhaul.
Zidane has already addressed the rumors of advances for Chelsea's Eden Hazard and Manchester United's Paul Pogba, and in March, the Real Madrid manager talked about his fondness for Mbappe.
With three goals against Monaco, Mbappe became the youngest player to record 30 Ligue 1 goals in a season, and the first Frenchman to do so since Jean-Pierre Papin in 1989-90.
PSG were crowned league champs for the sixth time in seven years earlier Sunday after Lille's goalless home draw to Toulouse.