PSG remain in discussions with Mbappe – who celebrated his 100th Ligue 1 goal on Sunday – over a new deal.
Varane was asked about France team-mate Mbappe ahead of Wednesday's World Cup qualifier at home to Ukraine, and he told Europe 1: "He's still young, but he's already progressed enormously and he continues to evolve.
"He's becoming more and more complete and he's still a goalscorer; he's one of the greats.
"I aspire to play with the best players and Kylian is one of the best players in Europe."
Madrid head coach Zinedine Zidane has made no secret of his desire to work with countryman Mbappe at the Santiago Bernabeu.
However, Zidane's future in the Spanish capital has been debated amid talk he could leave Madrid at the end of his contract in 2022.
Zidane returned to Madrid in 2019 after exiting a year earlier, having guided Los Blancos to three consecutive Champions League titles and LaLiga glory.
Taking charge of France has long been mooted, with Didier Deschamps' Les Bleus contract due to expire after the 2022 World Cup in Qatar.
"It's a possibility," Varane said of former international and 1998 World Cup winner Zidane coaching his native France.
"The French national team is a target for every French coach, it's normal that he’s potentially considered but it's not something relevant now.
"Our coach [Deschamps] is doing a very good job and we must focus on our short-term goals: clinching our presence in the World Cup and then the 2021 Euros."