The Chelsea man played a starring role in his nation's shock 2-1 win over Brazil on Friday that took them to the last four.
France and Mbappe already lay in wait, having dispatched Uruguay 2-0 in the day's earlier kick-off to book their own spot in the semis.
"Mbappe? I have spoken to him on the phone quite a few times," the Belgium playmaker explained to BeIn Sport.
"He watched footage of me when he was a kid. Now I watch footage of him! I have mad respect for what he does at his age. In modern football, it's unheard of."
Hazard is also wary of one of his Chelsea team-mates, whom he believes has no equal as a holding midfielder.
"I play all year with [N'Golo Kante. He is the best in the world in his position," he added.
"When he is at his best, you have a 95 per cent chance to win the game."
And despite the rivalry between the two neighbouring nations, Hazard confessed that France's previous World Cup-winning side made a big impact on him as a youngster.
"I grew up with 1998. We were maybe more France fans than Belgium at the time," he recalled.