Newcastle failed with an attempt in January and received the same response from Napoli this week, reports Calciomercato.com.
While the size of the Toon's offer was undisclosed, Napoli president Aurelio de Laurentiis is prepared to sell this summer for €100m.
Nigeria international Osimhen is also interesting Manchester United.
Osimhen has made 30 appearances for Napoli this season, scoring 17 goals and providing six assists.
His contract with the club runs until June 2025.
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