The 18-year-old winger is currently on loan at Scottish Championship outfit Inverness and is scheduled to return to Rangers in January.
The winger will be out of contract at the end of the season and Rangers could not reach an agreement on a fresh deal over the summer.
The Glasgow giants want to keep hold of the talented young winger and it has been claimed that fresh talks are scheduled to take place between the club and his representatives soon.
Rangers are feeling optimistic about their chances of convincing the teenager to put pen to paper on a new contract.
But the pressure is on Rangers as the player is just a month away from having the option of agreeing on a pre-contract with another club.
It has been claimed that his preference has always been to stay at Rangers and he is likely to stay if he is promised game time in the first team.
There were disagreements between the club and the player when the failed talks happened last summer and it led to him being demoted to the B team.
But it has been claimed that Rangers have changed the person who will be handling the negotiations with Kennedy’s representatives.