The 23-year-old Nigerian is reportedly bewitched by the Premier League and wants to play in the English top-flight soon.
Napoli would consider selling him in the summer if a club decide to match their €100m asking price, which is likely to deter several teams.
Manchester United are interested in him and are not worried about Napoli’s financial demands with suggestions that they are preparing an offer, while Newcastle United are also keen.
And it has been claimed Osimhen is also on the radar of north London club Tottenham this summer.
Antonio Conte wants to bring in half-a-dozen new recruits into his Spurs squad this summer and getting a striker is one of his priorities.
Osimhen has been watched by Spurs and the club considered signing him when he was at Lille.
Napoli’s asking price is likely to worry Spurs, who may be unlikely to have the funds needed to spend €100m on a single player.
Spurs would though have the added attraction of Champions League football attached to them if they get a point at Norwich on Sunday.