The prolific forward has caught the attention of Manchester City and Juventus with his excellent performances for the Partenopei, but Bigon has made it clear that the Uruguayan is not for sale under any circumstances.
"I can confirm that Cavani is not for sale at any price. The president has made it clear to everybody how he feels about a transfer," Bigon was quoted as saying by Corriere dello Sport.
"And Edi, too, has been very clear about his intention to stay at Napoli.
"We don't have any meetings scheduled [to discuss his future]. There's no need to talk about it. We have a very close relation with Edinson."
Roberto Mancini is thought to be extremely interested in the 2011 Copa America winner, as well as Colombia hitman Radamel Falcao.
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Goal.com understands that City have been in contact with the Serie A club over the past two summers, and were thought to be confident of prising him away this time around after the Partenopei failed to qualify for next season's Champions League.
The 25-year-old, who joined Napoli from Palermo in the summer of 2010, has a contract that runs until 2016, but the Premier League champions are willing to make a big-money signing once they offload up to four first-team players.