The 19-year-old, who joined Madrid from Lens in 2011, has started just eight league matches since moving to the club.
It had been reported that Manchester United were preparing a move for the Frenchman in the next transfer window, but Varane has insisted that he will not leave the Bernabeu.
"You could have the impression that I have not made much progress. But it is false. Clearly we all have to evolve quickly, perhaps more quickly, than we might have done before," he told reporters.
"This has created some impatience, both for you and me. But for the moment I do not have reason to think about a transfer."
Varane has yet to make his international bow for France.