The highly-rated Frenchman is said to be unhappy at the Bernabeu and is considering his future, which could allow the Blues to swoop for his services.
Varane made his debut for Real Madrid under Jose Mourinho who is now in charge at Chelsea, and that could play a key role in the young defender's future. He slipped down the pecking order following Mourinho's departure, behind Sergio Ramos and Pepe, and is now said to be seeking clarification over his future in Spain before making a decision about where he will be next season.
According to the Standard, Chelsea have made initial contact with Madrid, making enquires about Varane's potential availability and how much he could end up costing. Given how highly he is rated, the former Lens defender is likely to cost Chelsea a pretty penny.
Part of the reason for Varane's apparent unhappiness at Madrid is that he's on £25,000-per-week, which is much lower than the majority of his team-mates. Chelsea may be able to lure him to west London with the promise of a much higher wages.
It has previously been claimed that a £20 million bid could be enough for the 21-year-old, who is considered the man to replace Luiz.
The Blues have been active in the transfer window so far, bolstering their midfield by landing Cesc Fabregas and adding to their front line by sealing a £32 million deal for Diego Costa.
Filipe Luis has arrived to take Ashley Cole's place at left-back, but they still seem a little short at the heart of their defence. The Blues sold Luiz to Paris Saint-Germain for £50 million earlier this summer, leaving Gary Cahill and John Terry as first-choice centre-backs.
Problems at the back
Behind that pair Chelsea can call upon the services of Kurt Zouma, who is yet to make a competitive appearance for his new club, and Branislav Ivanovic, who is needed to occupy the right-back position.
Chelsea appear keen on trying to make it clear that their spending is done, but if is unlikely that Mourinho won't at least consider adding another centre-back before the window slams shut.
A striker is likely to be on the agenda as well, especially if Fernando Torres and Romelu Lukaku are sold - which recent reports suggest they could well be.