The Reds defender has been linked with a switch to Real Madrid this summer, but the Northern Irish boss has said that the club will be doing their utmost to secure the England international to a fresh deal at Anfield.
He told the Liverpool Echo: "We want to keep Glen here. 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.
"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.
"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."
The Reds host Sunderland on Wednesday.