Real are two points behind the leaders after victory over Almeria.
Varane said: "We'll continue giving it everything until the end of the season and will try to win all our remaining games in order to put pressure on Barcelona. We are going to battle until the end. We are focusing on our upcoming games, we'll see what happens afterwards.
"I've been playing more regularly in 2015 because of injuries but also because of technical decisions. I always try to give it my all for the team and I'm really happy. I'm part of the manager's plans and if I'm able to help the team, then all the better. I try to repay the manager for the confidence he has shown in me. I'm in great form and hope to maintain this level until the end of the season."