Varane has been on Uniteds radar for several years and Jose Mourinho failed with his attempt to lure the France international to Old Trafford.
But speaking after Frances 4-1 win over Moldova on Friday evening, Varane has stressed that he is not pushing for a move away from Madrid.
To say that I am not happy at Real Madrid is not true, said Varane.
Im at Real Madrid. The biggest club in the world.
Im constantly in a state of challenging myself because the requirement here is that of the highest level.
Im focused on my career. We had a tough time in the middle of the season where we had to fight. Ive given my all in this shirt and I can be proud of that.