The 27-year-old moved to the Yellow Canaries on a free transfer at the conclusion of the 2022-23 term following a five-year spell at Rangers in the Scottish Premiership.
Kent has struggled for regular first-team minutes this term, starting just one league match and playing only 134 minutes of Super Lig football since the beginning of the campaign.
The winger was formerly on the books of English giants Liverpool after graduating through their youth system, however he was never able to cement a spot in Jurgen Klopp's squad.
According to TEAMtalk, Kent had a suitor for his services from the Premier League during the final stages of the January transfer window.
The report claims that Vincent Kompany's Burnley submitted an offer for the attacker, who has not featured for Fenerbahce since late November.
It is understood that the Clarets launched a loan bid for Kent's services for the remainder of the term, however it was the player himself who turned the deal down.
Looking for a permanent move away from the Istanbul-based club, it is believed that the former Bristol City loanee was not pleased with the temporary nature of the agreement.
It was reported that fellow Premier League outfit Sheffield United were also keen on Kent, with the Blades desperately attempting to save their first-tier status under Chris Wilder.
It appeared as if the ex-Rangers man was on his way to Serie A on the closing day of the winter window, before a switch to Lazio collapsed.
With Kent's contract supposedly 'frozen' at Fenerbahce, it is said that manager Ismail Kartal will be unable to use the winger for the remainder of the season.
The Yellow Canaries have not required the talents of Kent in recent times, with the Istanbul club sitting top of the Turkish Super Lig standings, level on points with second-placed Galatasaray.
Burnley's January arrival David Datro Fofana netted a brilliant brace to rescue a point against Fulham on Saturday afternoon, with the Clarets facing a trip to Anfield where Liverpool await this weekend.