Defeat to Bologna and Conte's angry post-match reaction sparked speculation that the coach could be on his way as early as this week.
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But De Laurentiis took to social media last night to rubbish the reports.
He posted to X: "To the fans who have read some stupidity, I would say: I am proud to have a man like Antonio Conte by mine, the club and the players' side.
"Conte is a man who, with great generosity and dedication, is able to sacrifice every second of his life for his work."
Napoli are now winless from their past three games.