Los Blancos have been consistently linked with a move for the French international as his contract in Paris winds down at the end of the current season.
Despite PSG insisting they remain confident over securing a renewal for the former AS Monaco forward, the signs look increasingly likely that he will move on in 2022.
Real Madrid are firm favourites to sign the 23-year-old, if he does move on, with reports from Marca claiming a move is imminent.
Despite missing out on him last summer, Real Madrid have remained determined to secure their No.1 transfer target this season, with extension talks at the Parc des Princes deadlocked.
As per the report, Mbappe is expected to sign a five-year deal in Madrid, including a potential signing on bonus of €60-80m, and a basic annual salary of around €25m.