The African footballer of the year has been linked with a move to the London-based club, despite a solid interest from Saudi Arabia club, Al Ahli.
However, Osimehen was not able to reach an agreement with the Premier League club on personal terms.
This, however, leaves the 26- year-old future up in the air, as he has been frozen out by Antonio Conte in Napoli after the Italian coach signed Romelu Lukaku to lead his attack this season.