Kent was named PFA Scotland Young Player of the Year after an impressive loan spell at Ibrox last season, in which the 22-year-old scored six goals.
He returned to Liverpool at the end of last season and featured throughout pre-season for The Reds, but his only senior appearance came in a 2-2 FA Cup draw with Exeter in 2016.
Kent took to Instagram last month to vent his frustration at Liverpool, quoting a a passage from the bible.
With the Scottish transfer window open until September 2, Kent will plead with Liverpool to allow him to join Ranger on a season-long loan with a view to a permanent deal, according to the Daily Record.
“When the English window closed without Ryan moving on, Rangers realised they may still have a chance of doing a deal but that they would have to be creative in order to make it happen.” A source told the Scottish outlet.
“Klopp has ruled out another straightforward loan but Rangers hope the additional clause, which would turn it into a permanent move at a future date, might help swing the deal in their favour.
“Ryan knows he’ll have to do everything he can to help make it happen and it seems that’s exactly what he is trying to do.”
Kent was left out of Liverpool’s Under-23 squad for their 3-0 defeat by Chelsea on Monday after starting the opening game of the season against Tottenham.
Last month, Rangers manager Steven Gerrard admitted Liverpool had been priced out of a move for Kent.
“The end of it? Where we are right now, yes. We respect Liverpool’s stance and we thank them very much for allowing us to work with Ryan for a year.
“We have obviously got a Liverpool player at the moment in Sheyi Ojo who has started very well.
“I had a good conversation on the phone with Jurgen a few days ago and we totally respect Liverpool’s position on it.”