The 33-year-old midfielder, whose current contract expires at the end of next season, has played a major role in the club's drive towards a first English League title since 1990.
"Steven will be one we look to get a contract to in the summer," Rodgers told the Liverpool Echo.
"With a year to go, it's something we will address. I believe Steven will play beyond 2015. He is a player who has really shown his qualities this season.
"Come the summer, he will still only be 34. Looking towards the future, I still think he's going to be a key part of our squad."
Liverpool has been Gerrard's only professional club and for most of his 16-season career, he has been its best player with his ability to take the game by the scruff of the neck with a surging run into the box or a thunderbolt strike from range.
This season, however, Rodgers has used him in a deeper role, allowing him to mastermind play from in front of the defence and help unleash Liverpool's pacey and potent strikeforce.
"He has dropped into a new position and played it seamlessly. His intelligence in the game is second to none. He is improving all the time," Rodgers added.
"It's one where he has been brilliant for me as a captain and as a player this season and I would like that to continue.
"Most clubs, especially bigger clubs, recognise now that once a player gets over a certain age you have to look at a contract's duration.
"But for me Steven still has so much to offer and I really want him beside me here working on the field."
Rodgers said everyone at the club had felt empathy for Gerrard after his slip in the crunch match against Chelsea last weekend helped the Londoners to a 2-0 win that blew open the title race.
Liverpool will be looking to keep their title hopes alive in their penultimate match of the season against Crystal Palace on Monday and Rodgers expects Gerrard to put last week's costly error behind him.
"There is no blame attached to him because he has been instrumental in where we are to this day and he will continue to be in the coming years," Rodgers said.
"Steven has been brilliant on the training field this week. He has narrowed his focus like the team has and now we're looking forward to playing Crystal Palace."
Liverpool (80) lead Chelsea (78) in the standings by two points with two matches remaining and Manchester City (77) lie a further point adrift but have a game in hand as well as a superior goal difference to both sides above them.
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