Goal reported on Thursday that the Blues had hoped to offload the Nigeria international on a permanent deal during the January transfer window after he fell down the pecking order at Stamford Bridge.
The 28-year-old is understood to have turned down the chance to move to the Chinese Super League, but Chelsea eventually buckled and afforded him the chance of a temporary move.
Moses, whose current deal with Chelsea runs until 2021, was a key part of ex-Blues boss Antonio Conte's 3-4-3 system, but has found opportunities limited since Maurizio Sarri's arrival.
With Sarri having a preference for 4-3-3, Moses has appeared only five times since the Italian took over at Stamford Bridge, deployed as a wide forward rather than at wing-back.
Fenerbahce are slumped in 15th place in the Turkish Super Lig, struggling badly for form having won only three league matches this term, and will hope Moses' arrival injects fresh impetus into the side.
Just two points off the bottom of the table, the Istanbul giants are in serious danger of relegation.
Michy Batshuayi was also looking likely to join him, but with Thierry Henry's future up in the air it seems movement has ground to a halt.
Indeed, Alvaro Morata's move away from London is being held up by the goings on at the principality club, with the Spaniard having been on the brink of signing a deal with Atletico Madrid.
The Spanish side had been in talks with Monaco over a move for Gelson Martins, but with the Ligue 1 side in disarray things have become more complicated.
Gary Cahill and Danny Drinkwater have also been deemed surplus to requirements and are likely to be let go if the right offer arrives.