The Brazilian centre-back has become a regular fixture at the heart of the defence for the current LaLiga leaders making 30 appearances this season in all competitions.
Chelsea meanwhile could be in need of defensive reinforcement this summer with Antonio Rudiger , Andreas Christensen and Cesar Azpilicueta all in the final years of their contracts.
It's said that the Blues intend to probe the Spanish giants with a call at the end of the season in order to please their German manager.
Militao is currently contracted at the Santiago Bernabeu until 2025, but is said to be one of their lowest earners earning €3m (£2.5m) a year.
After a difficult start to life at the club, this season he has become of their more integral assets.
Chelsea could find it difficult to persuade Madrid to sell and Militao is happy with life at the team who sit four points clear at the top of LaLiga.
The Blues attempted to bring in a centre-back during the last summer transfer window in the form of Sevilla's Jules Kounde.
They came close to signing the Frenchman but Sevilla's sporting director Monchi then agreed to manager Julen Lopetegui's request to keep the 23-year-old.
Chelsea hope to extend the contracts of Rudiger, Christensen and Azpilicueta are running out of time before their current deals expire in the summer.
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