According to BT Sport presenter Darrell Currie, Liverpool "have no interest" in sending the player out on another temporary deal.
The 22-year-old has already amassed five loan spells. Before Rangers he spent time with Barnsley, Bristol City, Coventry City and Freiburg.
His future at Liverpool has yet to be decided with manager Jurgen Klopp keen to witness the player up close during pre-season.
It is likely going to take a "sizeable" bid and the player's desire to leave for an exit.
Currie tweeted: "As it stands Liverpool have no interest in loaning out Ryan Kent again. Klopp wants to see him in pre-season to assess his development. Things might change later in the window but Kent himself will have to push very hard to make this happen.
"A bit more on Ryan Kent: If a sizeable bid was made and Kent himself wanted to go then Liverpool would be more inclined to sell. Over to the Rangers board..."
Rangers boss Steven Gerrard has called on the player to do his part if he wants to rejoin the club.
He said: "I can assure the fans we’re doing everything we can to try to get Ryan back. The key thing that people need to understand is that Ryan has got to want this.
“It’s all right the fans wanting him, the staff wanting him, myself wanting him. But it’s Ryan’s decision.
“He’s got to want Rangers, he has got to want to come and be successful at Ibrox. That is the question Ryan has got to ask himself."