The Poland international is currently on-loan at Roma, though the Giallorossi aren't expected to seek a permanent deal at the end of this season.
In contrast, Napoli president Aurelio de Laurentiis wants to keep Szczesny in Italy and has tabled a five-year contract offer to his agents for consideration, says Sky Italia.
De Laurentiis is also in talks with Arsenal, pushing the Londoners to drop their €20 million asking price.
For his part, Szczesny is open to extending his career in Serie A next term.
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