Cech, who has been with the Blues since 2004 has enjoyed another fine campaign, and was voted on to the PFA Team of the Year last month.
However Courtois, who has been on loan at Atletico Madrid for the past three seasons, has a burgeoning reputation as one of the best young 'keepers on the planet - a fact emphasised by his stunning performance that helped dump Chelsea out of the Champions League at the semi-final stage last week.
According to the Sunday Times, Mourinho is gearing up for a summer shake up at Stamford Bridge - part of which will see Courtois return from his three-year spell in Spain and take up the gloves in goal for Chelsea.
The paper adds that Mourinho is concerned that he could lose Courtois if he doesn't bring him back to Chelsea soon given that he only has two years to run on the contract that he signed when he joined the club from Genk in 2011.
That would make Cech's future at the club uncertain. The 31-year-old has been unchallenged between the posts at Chelsea for the last ten years and given his age he may well consider a move away to continue his career at the top level.
Alongside the switch in goal, Mourinho is said to be willing to let playmaker Oscar go after his dip in form over the second half of the season, while a deal for Atletico Madrid forward Diego Costa is still on the cards.