The Belgian stopper, currently on loan at Atletico Madrid, has recently been linked with a move away from Stamford Bridge.
However, Courtois has played down the rumours.
Courtois has an option in his loan deal to extend his stay at the Vicente Calderon by a further year, but it is believed that the Blues would like the youngster to gain Premier League experience.
According to talkSPORT, Saints manager Nigel Adkins is prepared to swoop for the keeper should his side win promotion from the Championship this season.
The young goalkeeper, who made his debut for Belgium in October, moved to West London from Racing Genk last year.