The Turkish giants won the race to sign Kent on a free transfer last summer when he ended his association with Rangers.
While the expectation was that the Englishman would become a regular in the starting lineup, he has instead been limited to 15 appearances in all competitions.
Just one of his eight starts have come in Super Lig, while the 27-year-old has contributed just one goal and two assists.
As a result, Fenerbahce have been open to parting ways with the former Liverpool youngster throughout the January transfer window in a bid to bolster their FFP position.
At one point, Sheffield United looked like a potential location, but Sky Italia claims that Lazio have emerged as his most likely destination.
I Biancocelesti are said to have capitalised with Kent having had his contract 'frozen' by Fenerbahce, effectively forcing him into a transfer if he is to play football during the second half of the season.
Maurizio Sarri's side have also been linked with Plymouth Argyle's Morgan Whittaker, yet it appears that pushing through a deal for Kent is now more likely.
Lazio had been enduring a quiet transfer window despite sitting down in seventh place in the Serie A standings, albeit just two points adrift of fourth spot.
Kent is no stranger to plying his trade abroad with a loan stint at Freiburg back in 2017-18 also among his experiences.