The 22-year-old joined Napoli from Lille last September and has scored 17 goals in 38 appearances for the Italian outfit in all competitions, including seven in eight outings during the 2021-22 campaign.
According to Gazzetta dello Sport, the Nigeria international's form has attracted the attention of both Man United and Man City, while Paris Saint-Germain have also been credited with an interest.
The report, though, claims that Napoli president Aurelio De Laurentiis would only listen to offers in the region of €110m (£93m) for the in-demand attacker.
The Blues have Osimhen on a contract until June 2025, placing the club in a strong position when it comes to any potential negotiations.
Man City are still looking for a new striker, having missed out on Tottenham Hotspur's Harry Kane over the summer, while Man United are believed to be planning to target another forward in 2022 despite re-signing Cristiano Ronaldo before the end of the recent transfer window.