That’s according to a piece from the Daily Mail, who name the Clarets as one of a handful of teams tracking the Finland international, with the likes of Brighton, Leeds United, and Southampton also said to be keen.
Kamara started his career at Arsenal, but has flourished since he made a move to Scotland with Dundee.
After signing for the Gers in 2019, he has established himself as a key figure in Steven Gerrard's plans, and helped the Gers to a historic Scottish Premiership title win this term.
The 25-year-old has impressed on an individual level, and currently has the highest pass completion rate of any player in the Scottish top flight, as per Whoscored.
Luring Kamara away from Ibrox could be a tricky task, however.
Elsewhere, Eurosport report that West Ham are very likely to make a move for Turf Moor talent Josh Brownhill in the upcoming transfer window.
The 25-year-old is a central figure for Sean Dyche’s side, and has made 26 top flight appearances already this term.
The ex-Bristol City man is in the Clarets’ top five highest-rated performers this season, as per Whoscored, and it would appear that his displays have not gone unnoticed, with suggestions that the Hammers are determined to take him to the capital in the coming months.
We’ve gathered the best of the rest of today’s Premier League speculation below:
. BURNLEY, ENGLAND - MARCH 06: General view inside the stadium as Nick Pope of Burnley takes a goal kick during the Premier League match between Burnley and Arsenal at Turf Moor on March 06, 2021 in Burnley, England. Sporting stadiums around the UK remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Clive Brunskill/Getty Images)
Turf Moor. (Photo by Clive Brunskill/Getty Images) Photo: Clive Brunskill
. Kenny backs Lennon for Blades job
Neil Lennon is an ideal candidate to be the next Sheffield United manager, according to ex-Blades stopper Paddy Kenny. (Football Insider) (Photo by Ian MacNicol/Getty Images) Photo: Ian MacNicol
1. Kenny backs Lennon for Blades job
Neil Lennon is an ideal candidate to be the next Sheffield United manager, according to ex-Blades stopper Paddy Kenny. (Football Insider) (Photo by Ian MacNicol/Getty Images) Photo: Ian MacNicol
2. Bull wants McBurnie at Wolves
Wolves legend Steve Bull has claimed that Sheffield United striker Oli McBurnie would be a good signing for his former club. (Transfer Tavern) (Photo by Clive Rose/Getty Images) Photo: Clive Rose
3. Bent backs Toon swoop for Townsend
Former Premier League striker Marcus Bent has suggested that a return to Newcastle United could be a good move for Crystal Palace winger Andros Townsend. (Football Fancast) (Photo by Matthew Childs - Pool/Getty Images) Photo: Pool
4. Brighton and Burnley track Kamara
Brighton and Burnley are among the clubs interested in signing Rangers midfielder Glen Kamara this summer. (Daily Mail) (Photo by Ian MacNicol/Getty Images) Photo: Ian MacNicol