Jose Mourinho is known to be a massive fan of the 20-year-old centre-back after coaching him at the Bernabeu and handing him his first real taste of first-team football at the club.
He has since remained keen on the Frenchman, and is now ready to make a big move to lure him to London at the end of the season.
Varane has struggled with injury problems since bursting onto the European scene in 2011, which has led to concerns from Real that he may never live up to his true potential.
Mourinho however is convinced otherwise, and is even willing to risk £25m on the classy defender.
The player himself has admitted that he’s happy in Madrid, but he is known to have a fondness for Mourinho after working under him.
Chelsea are thought to remain on the lookout for defensive reinforcements despite having already sealed a deal for Kurt Zouma, with the futures of John Terry and David Luiz unclear.