The England captain, who has just 18 months left to run on his current deal, has spent his entire career at Anfield.
However, Rodgers says that he has discussed the possibility of a contract extension with the Reds skipper but nothing has been decided as of yet.
"Steven and I have spoken a number of times [about a contract], but as yet I don't believe anything has been done," Rodgers told The Mirror. "His feeling the last time we spoke was get through this season and see how that goes.
"His focus is on really helping the group to go forward.
"There's no doubt that between now and the end of this season the contract will be looked at."
Liverpool travel to the Emirates Stadium to face Arsenal tonight.