The two players are the two most expensive footballers in history, with the former switching to Paris Saint-Germain from Barcelona and the latter arriving from Monaco.
Neymar has scored 32 times in his 35 appearances for PSG, while Mbappe has managed 25 goals in 47 appearances for the French giants in all competitions.
Los Blancos did not directly replace Cristiano Ronaldo during the summer transfer window, and according to AS, the European champions currently have as much as £330m to spend on new players.
Julen Lopetegui's side have started the post-Ronaldo era with three straight La Liga wins, and will be looking for a fourth when they travel to Athletic Bilbao this weekend.
Neymar and Mbappe, meanwhile, will both be in action when PSG host Saint-Etienne on Friday night.