Gordon was out of favour when Rodgers first arrived at Parkhead but has now cemented his place in the first team and the Celtic boss is keen to keep hold.
The 34-year-old has a deal until the end of the season but there is the option of a further 12 months, something both parties are keen to activate.
"Craig is definitely one I want to keep," Rodgers said. "You see now a different goalkeeper to when I first came in. How sure, how calm he is - and there is another clean sheet he got last Saturday (against Hamilton).
"He still has a lot of games in him. He’s 34 soon but he’s a top goalkeeper who looks after his body, lives his life the right away. Guys like Edwin van der Saar go onto 40. He has a good few years left."
Gordon is also happy, and when asked if he wants stay, he said: "Yes. There’s no rush and I’m happy with what the situation is. But I’m happy for it continue the way it is."