The Spanish giants are rumoured to be looking at the Blues stopper amid talk that he could be offloaded before the summer transfer window closes following Thibaut Courtois’ return to west London.
Although Jose Mourinho wants to keep both glovesmen at Stamford Bridge, he is aware that neither is ready to sit on the bench.
And with the Belgian at the start of what looks likely to be a long and successful career, Cech’s presence is no longer a priority.
Real are keen to snap him up after losing faith in Iker Casillas, but Chelsea will look to use the situation to their advantage.
Mourinho is known to be a long-term admirer of Varane, whom he rates as one of the best centre-back in European football after coaching him at the Bernabeu having signed him from Ligue 2.
Los Blancos are far from keen to sell, but they may relent and accept a player plus cash deal if the young Frenchman shows a willingness to head to England, which he may amid a pay dispute at the club.