The 24-year-old has established himself as one of the star names in world football during his stint in Naples.
Since 2020, Osimhen has contributed 65 goals and 15 assists from just 111 appearances, helping Napoli end a wait of over three decades for another Serie A title.
However, the Nigeria international has entered a stage in his contract and career where decisions needs to be made over his next move, the player having just over 19 months remaining on his deal.
Furthermore, there was a well-documented fallout over two offensive Tiktok posts made towards Osimhen by the club's social media team earlier this campaign.
As it stands, the likelihood is that Osimhen will remain at Stadio Diego Armando Maradona for the remainder of 2023-24, Napoli hoping that he can at least keep the club in the top four of the table even if they already sit 10 points adrift of leaders Inter Milan.
Nevertheless, if Osimhen reaches the summer with just a year on his contract, president Aurelio De Laurentiis will begin to consider offers for his signature.
According to the Evening Standard journalist Nizaar Kinsella, Osimhen's preference would be to sign for Chelsea.
The likes of Arsenal and Tottenham Hotspur have also been linked with the frontman, as have Manchester United but at a time when they may not be able to afford the player.
Osimhen is seemingly more interested in a switch to Stamford Bridge, though, and the transfer may become a possibility in the summer, rather than January.
Recently, club legend John Obi Mikel acknowledged that he would like his Nigerian compatriot to move to the West Londoners, offering to help with any negotiations.
Pochettino already has Christopher Nkunku, Nicolas Jackson and Armando Broja has options in the final third, that trio all having admirers in the Argentine.
That said, Chelsea have not always looked clinical in attack, and being able to sign a player of Osimhen's stature for less than his market value - given his contractual situation - may prove too appealing to turn down.