The Belgian goalkeeper has just finished his third season on loan at Atletico from parent club Chelsea, who he has not yet represented in a first-team match.
As it stands, the 22-year-old is due to return to Stamford Bridge this summer, but Gil has said that the youngster wants to remain in Madrid.
"Courtois wants to stay and he's told the directors that. But it all depends on him and Chelsea have an injured goalkeeper," Inside Spanish Football quotes Marin as saying.
Atletico were beaten 4-1 by Real Madrid in the Champions League final last night.