The Gunners had an initial bid of €65m rejected by the Serie A side earlier this week as they eye a replacement for Alexandre Lacazette.
Arsenal are now prepared to go to €100m for Osimhen, but will face competition from Tottenham.
Local journalist Lorenzo Amuso told Calciomercato.com: “(Antonio) Conte, thanks to the Champions League qualification, has obtained great guarantees on the transfer market, so we can expect really great things from Tottenham.
"Among the names, there is Osimhen of Napoli.
"Tottenham is not the only club that has taken an interest. Arsenal have already presented a €60m offer, rejected by [Aurelio] De Laurentiis [Napoli's owner]."
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