Mbappe, whose contract expires this summer, informed PSG president Nasser Al-Khelaifi of his decision on Tuesday.
PSG anticipates that Mbappe will make the move to Real Madrid at the conclusion of the season, pending the finalization of his departure terms.
The negotiations between the two parties will determine whether Mbappe will depart for a transfer fee or forgo his own earnings. Mbappe has assured PSG that he will not depart on a free transfer.
Real Madrid has maintained a keen interest in the 25-year-old forward for some time, although he would need to accept a reduced salary to join the Spanish club, despite their willingness to offer him the highest salary in their history.
PSG rejected a €220m (£188m) bid from Real Madrid for Mbappe in August 2021. Following that, the forward opted to extend his contract with PSG for three years, which expires this summer.
If Mbappe choose to extend his contract for an additional year, PSG would value him at €150m (£128m) in the upcoming transfer window. Last summer, they accepted a €300m (£256m) bid from Saudi club Al Hilal, which Mbappe declined.