The 24-year-old has been in excellent form for the Blues during the 2022-23 campaign, scoring 28 goals and registering five assists in 37 appearances in all competitions.
Osimhen netted five goals in six Champions League appearances this term, while he has managed 23 goals and five assists in 30 Serie A appearances, with Napoli winning the title.
The Nigeria international made the move to Stadio Diego Armando Maradona from Lille in 2020, and he has represented Gli Azzurri on 99 occasions, scoring 56 goals and registering 14 assists.
Osimhen only has another two years left to run on his contract with Napoli, and there is currently a host of speculation surrounding his future, with a number of clubs said to be interested in his services.
Bayern Munich, Chelsea, Arsenal and Paris Saint-Germain have all been heavily linked with Osimhen, while Man United have also allegedly identified him as a leading target.
The Red Devils continue to be linked with Harry Kane, but Tottenham Hotspur chairman Daniel Levy is likely to resist a sale to a Premier League rival.
As a result, Osimhen could emerge as Man United's preferred option through the middle, and according to Il Mattino, Napoli are not against selling the Nigerian this summer.
However, the report claims that the 20-time English champions would have to offer €160m (£140m) to stand a chance of bringing the attacker to Old Trafford in the upcoming market.
Marcus Rashford is Man United's leading goalscorer this season, finding the back of the net on 29 occasions in all competitions, while Bruno Fernandes is second with 11.
Anthony Martial has only managed eight goals, though, and the Frenchman is widely expected to leave the Red Devils on a permanent basis this summer.
Wout Weghorst has managed just two goals since arriving on loan from Burnley in January, meanwhile, and he is unlikely to move to Old Trafford on a permanent basis.
As a result, there is a chance that two new forwards could arrive this summer, while head coach Erik ten Hag is also believed to want a centre-back and a central midfielder.
Osimhen's Napoli teammate Kim Min-jae is being heavily linked with a move to Old Trafford, with recent reports claiming that a deal to sign the centre-back is close to being completed.