The 32-year-old has been tipped to continue playing into his mid-30s, with a new contract offer expected to be put on the table in the coming weeks.
When asked by the club's official website if he expects Gerrard to end his career at Anfield, Rodgers said: "Yes, in my opinion. For sure.
"He said to me when I first came in that Liverpool was his club and when he retires from here one day, he'll still be a supporter of Liverpool. I've got every confidence.
"Between now and the end of the season we'll sit down and look at extending that because he's very important to the future here. That will then hopefully see him through and he can still win trophies here at Liverpool, which is important."
Gerrard, who had offers from Chelsea and Real Madrid during his career, has been at the club since he was eight years of age.