The Finland international's current deal expires in 2023 but the club are keen to tie him down before he enters his final year amid interest from England and abroad.
Gers boss Steven Gerrard is a huge fan of the influential midfielder, who was signed from Dundee for a bargain £50,000 in January 2019, and revealed the 25-year-old’s advisors are happy with the terms on offer, with the final decision now down to Kamara.
"He's extremely important to keep at the football club," Gerrard stressed.
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"His progress since we took him in from Dundee has been clear for everyone to see. He's gone on to become a real established international player. We know he can handle any football game here.
"I love the kid and the player and I've made it abundantly clear how much I want him to stay from a personal point of view.
"There's a real strong, good offer on the table for Glen so the speed in which this happens is totally on Glen. The ball is firmly in his court.
"The offer is really good from the club. His advisors are happy with the offer so now it's totally down to Glen. We're ready, waiting and hoping that it's done as soon as possible."
Kamara, who started all his country's matches at Euro 2020, will return to the Rangers squad for Sunday's trip to Dundee United after missing the midweek Champions League defeat to Malmo due to suspension.