Gerrard officially ended his 14-year association with England earlier this week, citing a desire to focus on his club side as a primary reason for stepping down as skipper of the Three Lions.
In a season that includes a Champions League football, Reds fans were largely supportive of the decision, and Rodgers is no different.
The Reds midfielder has just 12 months remaining on his current deal, but the Northern Irishman revealed that an extension is imminent.
He told the Liverpool Echo: "I am very happy that Steven is now going to commit to Liverpool and I am sure that [his contract] is something that we will look at.
“He is in real good condition and I’m sure it is something that will happen at some point. Listen, for his own mind, I’m sure he will want it sorted out, absolutely. You never want to leave players with not too long to go on their contract."
“A lot has gone on at the club over the course of the summer. It is something I am sure will get sorted.”
Gerrard turned 34 shortly before the World Cup, and Rodgers altered his captain's position to a more deep-lying midfield role last season in an attempt to prolong his career.
And Rodgers indicated how Gerrard's decision to end his playing career with Roy Hodgson's side will benefit the five-time European Cup winners.
“I know that Steven can continue to play on beyond this season. I have always said that,” Rodgers added.
“Now he doesn’t have international football, he will have that freshness. I think it is something that will be looked at by the club.”
Liverpool began their tour of the United States with a 1-0 defeat to Roma at Fenway Park in Boston, and Rodgers' side continue their pre-season preparations with a game against Olympiacos on Sunday.