The 29-year-old is set to enter the final 12-months of his contract, but he is a key figure in Rodgers' first-team squad.
"Glen is a player we want to keep," Rodgers told the Liverpool Echo.
"In terms of his contract, I am sure that is something that will be discussed between now and the end of the season.
"I think Steven Gerrard went down to the last year of his contract last summer before that was sorted.
"I'm sure it's something the owners will take up when the time is right. At this moment in time I am only really concentrating on the football aspect.
"We are all fighting to be best that we can be for the club."
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