Real are regarded as favourites to land the Belgium international, who has made it no secret he pines to return to Madrid where his former girlfriend and their children now live.
However, Don Balon says PSG are also interested in Courtois and are prepared to offer him a superior contract to convince him to delay his return Madrid.
Interestingly, Courtois' former club Atletico Madrid are eager to see such a deal happen. Atletico know PSG are also keen on their keeper Jan Oblak - but that interest would be shut down if they were to sign Courtois ahead of Real Madrid.
Just last week, the Chelsea keeper remarked: "I'm not clear about my future, what I said that my heart is in Madrid was misunderstood, although I have two children in Spain, in Madrid, and that's not easy, I have one year left and I'm happy and talking to Chelsea.
"They have bet on me from the first moment and that is not forgotten, I do not think Florentino Perez calls me, he will call my agent and he will listen to him."