The Blues have already agreed to sign centre-back Kurt Zouma from Saint Etienne, but they plan to add another high-profile stopper to their ranks in the summer transfer window.
According to O Jogo, Real Madrid defender Raphael Varane is the number one name on their wish list.
Chelsea boss Jose Mourinho rates the player highly having coached him at Santiago Bernabeu and he recently revealed he believed the Frenchman was the best defender in world football.
Prizing the youngster away from Real Madrid will be no easy task, although there is every chance the player will be tempted by the prospect of joining the Blues having seen little playing time of late.
Chelsea play host to relegation-threatened Norwich later today looking to keep their title hopes alive, and the Blues are available at 1/5 to claim maximum points.