Mbappe, still only 24, claimed the Golden Boot award at the 2022 World Cup after becoming the first player to score a hat-trick in the final in 56 years.
He hit eight goals across the competition, following up his four as France won the World Cup in 2018.
Real's interest in Mbappe has been well documented and they look like they were about to secure his signature on a free transfer in the summer of 2021.
They had already submitted three offers, the highest of which was €200 million, in the summer of 2021.
However, Mbappe, to the surprise of many, then committed his future to PSG by signing a new lucrative two-year contract with the option of a third.
He even said thanks to Real's supporters and hoped that they understood his decision to remain in the French Capital.
But the former Monaco man has looked every bit a Real Madrid player ever since he burst onto the scene and it seems president Florentino Perez will do absolutely anything to have him play for Los Blancos.
In fact, Gazzetta say the 14-time European champions are willing to fork out an overall fee of £877 million over a four-year period.
A large chunk of the eye-watering sum would be the wages, said to be a whopping £552 million, as well as a £132 million transfer fee and other signing on and commission fees.
Mbappe is out of contract in 2024 and can essentially walk way from PSG if he wishes as the final year is entirely optional.
Real are still very much swooping and hope to convince him to move to the Santiago Bernabeu by the summer.
Real legend Guti has urged the La Liga winners to make a move for Mbappe, who he believes is "made" for the Club.
"The best have to play at Real Madrid," he said, as per Gazzetta.
"Seeing him play for PSG makes me angry, and not only for Real but also for La Liga. La Liga must always have the best in the world."
"Mbappe is a player made for Real, and then if he wants to do what Lionel Messi and Cristiano Ronaldo have done, he has to play for Real Madrid because he won't make it for PSG."
"Madrid must go and get him immediately, now."