Gerrard proved the matchwinner against Aston Villa yesterday.
"Can Gerrard play on into his late 30s? Absolutely, no question," said Rodgers.
"Guys who do that like Giggs, Scholes, McAllister, it is not what they are doing now, it is what they have done earlier in their careers, when they were 17, 18, 19, 20.
"That's what allows you to play on. Gerrard has every chance to play on into his late 30s.
"He is 32 and wants to improve, he is England captain and wants to improve. He is still looking at areas he wants to improve on and just his enthusiasm to play football is remarkable."
As regards a new deal, Rodgers said: "A new contract is something on the agenda. It will happen in due course."