The defender has reportedly been lined up by Jose Mourinho as a replacement for David Luiz but he insists his priority is the World Cup with France
The central defender has been tipped to reunite with former Real boss Jose Mourinho at Chelsea after David Luiz agreed to depart Stamford Bridge for Ligue 1 champions Paris Saint-Germain.
Varane was an ever-present during Mourinho's final season in charge of the Madrid club, who eventually finished second behind Barcelona in 2012-13.
But the 21-year-old is not thinking about his club future as Didier Deschamps' France prepare to face Switzerland, Ecuador and Honduras in Group E at the World Cup in Brazil.
"Right now, I'm not thinking about (the interest from Chelsea), we have the World Cup ahead of us," Varane told French football programme Telefoot.
"We have a young, motivated team that can do great things and has no limits.
"I love the national team and contribute everything I have to them. My goal is to become a starter.
"(Real Madrid assistant Zinedine Zidane) knows what it means to win the World Cup and it's great talking to him about it."
While he refused to shed much light on his future, Varane was prepared to reflect on Real's triumphant Champions League display.
Real claimed their 10th European crown after overcoming La Liga champions and city rivals Atletico Madrid 4-1 in Lisbon on May 24.
It was Real's first Champions League title since 2001-2002, when they edged Bayer Leverkusen 2-1 in Glasgow.
"La Decima is something magnificent," he said. "My team-mates have waited a long time for this.
"This is truly the highlight of my career. It was like I was in a bubble after the game. There was excitement and happiness."