Gerrard has excelled in a new deeper role this season, making 32 appearances and scoring 13 goals as Liverpool have stormed to the top of the Premier League title.
His current deal expires in June 2015, but Rodgers is confident the 33-year-old can contribute beyond next term.
"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.
"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.
"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."
Table-toppers Liverpool travel to Crystal Palace on Monday, though they could begin the game third in the table if Manchester City and Chelsea both win this weekend.
