The legendary manager is expected to place last season's Champions League and La Liga top scorer Mbappe at the very centre of his sporting project to restore domestic dominance.
Speaking to BOYLE Sports, who offer the latest World Cup odds, Malouda said: "I think they have the same kind of mindset where they want to prove that they are the best, and I think they have common interests.
"I think Mourinho is the right profile to maybe put some order in the Real Madrid team. He's a different manager now. He knows that he needs to engage and create a connection with Kylian Mbappe. I think he will try to build a system around him to allow him to lead the team. Most importantly, they both love football.
"They have the same passion and dedication to football. What makes them happy is results, and results mean winning trophies. This is the common objective they have."