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Dybala, 28, is currently a free agent after his previous deal with Juventus expired at the end of last season.
The Argentina international had reportedly verbally agreed on a new deal worth up to €10m (£8.5m) with Juventus earlier this year.
However, talks broke down amid reports Juventus had altered their proposal to the striker.
The Turin club eventually opted to let him leave on a free this summer after signing striker Dusan Vlahovic from Fiorentina in January.
Dybala is now considering his options ahead of the new season.
Jose Mourinho's Roma have reportedly offered Dybala a four-year contract worth €6m (£5.1m) per season.
Those wages would break a proposed self-imposed salary cap at Napoli.
However, the club was already considering breaking its salary rules to offer an improved contract to Kalidou Koulibaly, who is instead expected to join Chelsea.
It is also claimed that Dybala's image rights could prove to be a sticking point in any potential deal, with Napoli president Aurelio De Laurentiis demanding all players sign those rights over to the club when they join.
Inter Milan were also reportedly keen to sign Dybala, who scored 115 goals in 293 games during his seven-year spell at Juventus.
But their interest in the forward cooled after the club re-signed Romelu Lukaku on loan from Chelsea.
Nevertheless, Dybala appears to have several offers to remain in Serie A for the new season, which gets underway on August 13.