The 27-year-old joined the Turkish giants as a free agent following the end of his contract at Rangers, with the Yellow Canaries winning the highly-contested race for his services.
Since moving to Fenerbahce, Kent has struggled for regular first-team minutes, playing just seven Super Lig matches for Ismail Kartal's side.
Overall, the former Liverpool youngster has featured 15 times across all competitions since June, finding the net on just the single occasion.
It was reported earlier on Wednesday that Serie A outfit Lazio had emerged as a likely destination for Kent in the dying moments of the winter window.
However - according to transfer specialist Fabrizio Romano - the attacker's move to Italy has collapsed, leaving little time for another switch to be arranged before the deadline.
It is believed that Fenerbahce have 'frozen' Kent's contract, meaning that he would be unable to feature for the club in the second part of the campaign.
Maurizio Sarri's men are searching for attacking reinforcements before the window slams shut, with Lazio currently seventh in the Italian top flight.
It has been suggested previously that Premier League strugglers Sheffield United held an interest in the acquisition of Kent, although it remains to be seen whether the Blades could re-enter the hunt for the Englishman.
Fenerbahce were said to be very keen on offloading Kent during the current window, with the Yellow Canaries mindful of staying in line with FFP regulations.
Kartal's men are currently top of the Super Lig standings having lost just once in their opening 23 matches, sitting level on points with second-placed Galatasaray.
Former Manchester City poacher Edin Dzeko and summer arrival Sebastian Szymanski have represented the main goalscoring threats for the league leaders, limiting Kent to just 134 minutes of league action.
Aiming to extend their winning streak to three matches, the Yellow Canaries will make the trip to Antalyaspor on Saturday evening in the Super Lig.