The France international has formed a formidable partnership with Ramos in the heart of Madrid's defense during his nine seasons at the club.
He has been touted as a possible contender to take on captaincy duties when Ramos, who will turn 35 later this campaign, eventually departs the Santiago Bernabeu.
However, the World Cup-winning centre-back is not thinking about what the future holds and says Ramos remains an integral player for Madrid.
"For the future, it's difficult to plan," he told beIN SPORTS. "Real Madrid is a very, very big club with great players. What is important is that everyone plays their part in the team.
"When we won our titles, our Champions Leagues, it was as a team, with eleven leaders on the pitch each time.
"Sergio is a legend in Madrid. The future for the moment I do not project about it, but for sure Ramos is a very important player for us.
"What is certain is that we are very complementary with Sergio Ramos, in our way of playing.
"We have qualities that complement each other perfectly. We have been playing together for several years, so we know each other very well.
"In defense, it works in pairs and this understanding is very important. For the future, after the departure of Ramos, it is difficult to project yourself.
"I am a leader in my own way. With my teammates, I talk a lot before matches about tactics and positioning. We each have our own way."
Varane takes full blame for Madrid's last-16 defeat and is keen to quickly move on when the new campaign begins next weekend.
"For sure, that will not remain a very good memory in my career. It was a difficult game for me, this elimination," he said. "Immediately after the match I wanted to take responsibility.
"I made some mistakes, it cost us the victory. You had to digest and watch what is happening ahead, and think about what is happening.
"At the high level, we don't have time to think about it - we have to think about the next game. The days that followed were a bit difficult, I admit, but at the top level, you have to look ahead quickly."