On Friday, the saga involving the Nigeria international had been expected to conclude with Chelsea vying for his signature alongside Al-Ahli.
However, despite the constant speculation, Osimhen rejected a contract offer from Chelsea and did not press ahead with a switch to the Saudi Pro League.
Although there was potential for the 25-year-old to be reintegrated back into the Napoli senior ranks, head coach Antonio Conte has insisted that will not be possible.
As a result, Napoli have been left with the prospect of their most prized asset sitting out the first half of the season before attempting to resolve the issue in January.
Instead, transfer expert Fabrizio Romano has alleged that Napoli have found a solution through one of the European transfer windows that remain open.
Decision time for Osimhen
Romano says that Turkish giants Galatasaray have managed to successfully negotiate a season-long loan deal with their Napoli counterparts.
Galatasaray have reportedly agreed to cover Osimhen's salary in its entirety, said to be somewhere in the region of €10m (£8.42m) per year.
There would be no option for Galatasaray to push through a permanent deal at the end of 2024-25, something that may prove pivotal in convincing Osimhen to sign.
While the Turkish transfer window is open until the middle of September, Galatasaray need to register their squad for the Europa League by close of play on Tuesday.
A contingent from Galatasaray are said to have travelled to Naples in order to try to tempt Osimhen into a switch to Super Lig.
Who would Osimhen rival for a striking role?
Galatasaray are certainly not short of attacking options with Mauro Icardi, Michy Batshuayi and Dries Mertens the high-profile names in the final third.
Okan Buruk's side have netted nine times in three successive league wins, although they did lose to Young Boys in the Champions League playoffs.
With Buruk deploying a 4-2-3-1 formation, Osimhen's arrival would leave him with decisions to make in how he accommodates all of his big-hitters.