The 20-year-old midfielder has impressed since moving to Griffin Park in the summer, making 17 appearances for the Bees and scoring two goals.
Saville is yet to make a first-team appearance for Chelsea but is due to return to Stamford Bridge in the new year.
However, Rosler is hopeful of extending his deal beyond January.
He told the Fulham Chronicle: "George Saville has fulfilled our expectations. 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."
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