The France international has attracted interest from Europe's best teams, including Madrid, and Varane hopes he ends up at the capital club.
"Mbappe is a very good youngster with a huge potential," the France defender told Telefoot . "It would be a pleasure to see him here.
"In addition to that he is French, so he would be welcome. We will surely get the chance to discuss this."
His current team-mate Cristiano Ronaldo has enjoyed yet another stellar campaign, scoring 25 top-flight goals to help Madrid to their first La Liga title since 2012, while surpassing 100 Champions League strikes en route to the final against Juventus.
Ronaldo is aiming for a fifth Ballon d'Or, but there is growing support for legendary Juve goalkeeper Gianluigi Buffon to win it, and Varane was effusive in his praise for both players.
He said: "They are immense. They made history. Their duel in the next game will have an influence on the Ballon d'Or.
"We're not acknowledging enough how Ronaldo is making football history right now. I'm lucky to play with him."
Zinedine Zidane's men face the Serie A champions in Cardiff next Saturday as they seek to become the first side to retain the Champions League title.