Varane, 22, is one of the most highly-rated defenders in Europe, though he has often played second fiddle to Pepe and Sergio Ramos in big matches.
However, the centre-back has already captained France and became the youngest-ever player to wear the country's armband in a 3-0 victory over Armenia last October.
And new Sevilla signing Kakuta - who played alongside Varane at Lens - has backed his former team-mate to one day captain the La Liga giants.
"Varane has all of the attributes needed to be the future captain of Real Madrid," Kakuta, who signed a four-year deal with the Europa League winners on Thursday, told AS.
"I know him very well; when we started out at Lens, we would sit next to each other on the team's away trips. We're both originally from Lille and although he is a bit younger than me, I'd already heard a lot of good things about him.
"He played in central defence but also sometimes as a midfielder. When I made my international debut at youth level for France, he was in the side too and once I saw him, I knew right away that he was going to be a top player. What he has done so far hasn't come as a surprise to me at all.
"He has always been a very laid-back bloke and a very intelligent guy too; he knows what he is doing and I believe that he will become Real Madrid's captain one day in the future."