The Blues chief coached the 32-year-old during his time at the Bernabeu, and even elected to drop club icon Iker Casillas in favour of him.
With rumours suggesting that promising Belgian stopper Thibaut Courtois may be allowed to leave Stamford Bridge at the end of the season, Mourinho is thought to have made Lopez his top target to challenge Petr Cech for the number one jersey in West London.
The experienced glovesman is believed to have a good relationship with ‘The Special One’ and could be tempted by a move to England with pressure mounting for Casillas – the club’s captain – to be reinstated as first choice by Carlo Ancelotti.
Reports suggest that Chelsea have already contacted officials from Real to discuss a deal, which would more than likely be concluded at the end of the season.
It is expected that veteran back-up man Mark Schwarzer will leave the Blues once the current campaign has finished, while Courtois is believed to be keen on a move to a top Spanish side after impressing during an extended loan spell with Atletico Madrid.