Il Mattino says with the 31 year-old's deal running down this season, Stones' agents have approached Napoli about a move this month.
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However, Napoli have rejected the proposal - for now.
While the Azzurri have resisted the approach, the door remains ajar as the days of the January market count down.
It's suggested Napoli sports director Giovanni Manna could yet revisit the deal closer to the deadline.