The 26-year-old winger moved to Glasgow on a permanent basis in the summer of 2019 from Liverpool and has been a key player for Rangers.
Kent will be out of contract at the end of the season and is set to leave Ibrox in search of the next chapter of his career.
He has a host of clubs showing interest in him due to his expected free agent status and Fenerbahce are amongst them.
And according to Turkish daily Star, Fenerbahce’s offer to Kent is better than the offers he currently has from other clubs.
The Istanbul side want to make sure they win the race for the Rangers winger and have placed a lucrative proposal on his table.
It was recently claimed that Kent is happy with Fenerbahce’s offer.
Kent was not involved for Rangers in their 3-0 win over Celtic in the Scottish Premiership on Saturday.
It remains to be seen where the former Liverpool winger will be playing his football next season.