The Portuguese boss worked with his compatriot at the Bernebeu, signing him ahead of his La Liga title win in 2011/12.
Coentrao played a big role from left-back under the ‘Special One’, but was also often deployed in a more advanced role thanks to his electric pace and attacking instincts.
And it appears that Mourinho has not forgotten the 27-year-old, with a move at the end of the season on his agenda.
Manchester United are also thought to be tracking the Portugal international, but the lure of reuniting with his old boss at Stamford Bridge may sway the former Benfica star.
Real are believed to be ready to sell Coentrao this summer for around £10m-£15m.