The Northern Irishman came close to guiding the Reds to their first league title in 24 years last season, but they eventually finished two points behind champions Manchester City.
Rodgers, who helped bring Champions League football back to Liverpool following a five-year absence, took over from Kenny Dalglish back in 2012 after managerial spells at Watford, Reading and Swansea City and is planning a lengthy stay on Merseyside.
"I'm only 41, which is very young, and there are lots of things I want to achieve here at Liverpool," Rodgers told Spanish newspaper AS. "It's an incredible club and I hope to be managing here for another 20-odd years."
Rodgers, who is yet to win silverware as Liverpool manager, has also expressed a desire to one day work in Spain.