The England defender has just one year remaining on his contract but manager Rodgers confirmed that talks will be held at the end of the season to extend Johnson's stay.
Johnson, who moved to Anfield from Portsmouth in 2009, has played a key role in Liverpool's bid for the Premier League title this term, making 21 top-flight appearances, despite spending some time on the sidelines through injury.
And Rodgers revealed that retaining the 29-year-old's services was a "priority".
"We want to keep Glen here," Rodgers told The Liverpool Echo.
"There is no question about that, especially now he's in this form. He's 29 and we feel that he has still got good years ahead of him.
"No contracts will be looked at until the summer but his will be a priority for us, especially if he continues in the form that he's in."
However, Johnson is reported to be one of the club's top earners and Rodgers admitted that discussions would be needed to determine a more suitable wage for a player who will turn 30 at the start of next season.
Asked what role Johnson's age will play in contract negotiations, Rodgers explained: "It just means you just have to sit, debate and discuss what's best for the club and the player.
"The beauty of this is we want to keep Glen and Glen loves it here. We just need to find a solution which is good for both.
"If we can do that then the club will have a very good player for years to come.
"We have other players like young Jon Flanagan who only has one year left, while Jordan Henderson only has two years left. They have been great and we want to look at those contracts.
"That's something that will be for the summer. The players can do themselves no harm by continuing to play in the form they are in. The club will then take a close look at it."
Liverpool's hopes of being crowned champions were boosted by Saturday's 6-3 win over Cardiff City and Rodgers single out Johnson for special praise.
"I thought Glen was outstanding against Cardiff," the former Swansea City boss added. "He showed his strength and power for Daniel Sturridge's goal with how he executed that pass for Luis (Suarez).
"It's important for me with how we play that the full-backs can get up, join in and make runs in behind. We are seeing now the player we all know Liverpool had – which is one of the best full-backs in the world."
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