The French World Cup winner hinted that his future may lie elsewhere when he revealed at the end of last season that he wants more responsibility at PSG or “maybe somewhere else”.
The Ligue 1 champions are loath to lose the 20-year-old ahead of the 2019/20 campaign, but they could find it difficult to hold on to him for any longer than year.
However, Mbappe will probably need to submit a formal transfer request in order to seal a move to Madrid.
The former Monaco forward has spoken of his admiration for los Blancos in the past, and Zinedine Zidane’s return as manager will surely boost their chances of landing the hottest prospect in football.
Mbappe scored 39 goals in 43 appearances in all competitions last term, but PSG failed to win three of the four tournaments they competed in.