The highly-rated midfielder, 20, made the move to Griffin Park in the summer on a loan deal until January, and has so far made 17 appearances for the Bees.
Saville is enjoying his time with Brentford and Rosler has been impressed with his contribution.
Rosler believes there is still more to come and plans to speak to Chelsea about a longer deal, possibly even bringing him back next season.
"George Saville has fulfilled our expectations," said Rosler, quoted by the Fulham Chronicle.
"He is a great player and can be even better - there's great potential in him.
"He's hungry and he likes it here. We'll try to do something in January and maybe in the summer as well."