The Elland Road side want to add three wingers to Marcelo Bielsa's squad for next season and hope that the Champions League winners will see the benefits of Harry Wilson's loan with Derby County as a way of persuading Kent to be loaned out.
Re-signing Kent is one of Steven Gerrard's priorities this summer with the Daily Mail noting that the Ibrox side are frontrunners in the race for the 22-year-old.
A loan deal is the only likely solution with the player valued between £8million and £12million by Liverpool.
Kent emerged as a key player for Rangers last term with his exciting wing play.
The club retain an interest in another Liverpool attacker, Sheyi Ojo with a loan deal likely.