Real have been linked with a move for the 20-year-old over the past two years and missed out on his services when he joined PSG from AS Monaco last season.
However, after the departure of club-record goalscorer Cristiano Ronaldo to Juventus, the LaLiga giants have been left with a glaring weakness in attack - which returning coach Zinedine Zidane has reportedly instructed to rectify.
France Football, the publication that awards the Ballon d'Or title, has now revealed that Los Blancos are willing to spend €280m of their €400m transfer kitty on the highly-rated attacker.
Mbappe has scored 31 goals and registered 15 assists in 35 games across all competitions.