Kent is contracted to Liverpool until 2022 and his value is believed to be worth anywhere between £8-12 million.
Rangers therefore are hoping for another loan deal, though it now seems they will have to wait for such a decision with Liverpool deciding to give some of their star players time off.
Roberto Firmino will be granted an extended three-week break after the Copa America Final. The same period of rest is expected to be handed to both Mo Salah and Sadio Mane after the Africa Cup of Nations.
This will leave Liverpool short of attackers for both pre-season friendlies and training, making it unlikely that Kent will be allowed to go until his star team-mates return at the end of July.
Rangers are expected to begin their Europa League campaign this coming Tuesday with the first leg of their tie against Gibraltarianside St Joseph's.
The Light Blues kick off their Ladbrokes Premiership season with a trip to Kilmarnock on Sunday 4 August.