The Nigeria international, who was linked with Newcastle in the January transfer window, has shone with Napoli and boosted his stock in the process.
He struck 18 times for Napoli over the course of last season, despite missing a chunk of the campaign through injury, and is again attracting interest this summer.
It is suggested that Newcastle, as well as Arsenal, would be prepared to sign him this summer, but according to Italian daily Gazzetta dello Sport, Osimhen is clear about not leaving Italy.
Osimhen does not want to leave Serie A and will reject proposals which come from the Premier League; it has been suggested Newcastle would double his salary.
He helped Napoli to a finish of third in Serie A last term and the club will have Champions League football on the agenda next season.
Even if Osimhen was prepared to leave Italy this summer, his asking price could prove to be prohibitive.
Napoli supremo Aurelio De Laurentiis would want in the region of €100m to let Osimhen go.
And Newcastle continue to work with a strict budget, which they are set to deplete further next week when they sign Sven Botman from Lille.
