The Brazilian, out of contract at Arsenal next summer, has already signalled to his representatives that he would welcome a switch to Naples, with talks between the two parties said to date back to early June, reports La Gazzetta dello Sport.
He made 25 appearances in all competitions as Arsenal won the Premier League last season, contributing five goals, but has slipped down Mikel Arteta's list of attacking options and is reportedly willing to accept a pay cut to force the issue. Arsenal's own valuation of the 29-year-old sits at around €20m.
Any formal approach depends on Napoli first raising funds through outgoings, after a summer in which president Aurelio De Laurentiis' guiding instruction to sporting director Giovanni Manna has been simple: sell before buying.
The club have already spent €86.5m making permanent three loan deals - Rasmus Hojlund from Manchester United for €44m, Alisson Santos from Sporting for €16.5m and Lorenzo Lucca from Udinese - leaving little room to move for Gabriel Jesus without first offloading Romelu Lukaku, whose exit to Fenerbahce is closest to completion.
Napoli's original €12m asking price for the Belgium international has reportedly softened to somewhere between €7m and €8m including bonuses in order to get the deal done. A second sale, either Lucca - whose loan spell at Nottingham Forest last season did little to enhance his value - or winger Noa Lang, who has attracted interest from Ajax as they reinvest proceeds from Mika Godts' move to Paris St-Germain, would also need to be completed before an offer lands in London.
For all the defensive urgency elsewhere in the squad, a marquee attacking addition would send its own message to Napoli's Serie A rivals about the scale of the club's ambition as they target a genuine push in the Champions League this season.