Higuain's brother and agent, Nicolas, fuelled speculation last month that the prolific Argentine, who has two years left on his contract, would leave when he said Napoli were not sufficiently ambitious.
"I haven't spoken to the player," Di Laurentiis told reporters. "The only offer I've had was from the president of Atletico Madrid last month and I told him we couldn't do anything.
"He offered 60 million euros (£50.1 million) plus two or three players and I said no."
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Di Laurentiis has said that there is a 94 million euro buyout clause in his contract if Higuain, last season’s top scorer in Serie A with 36 goals, leaves early.
He also dismissed talk that the striker could move to Serie A champions Juventus.
"Even if Juventus were to come into the picture, they need Higuain's consent," he said.
"Would he be betraying Napoli? It would be a much bigger betrayal of himself. You don't go to the Napoli curve (hardcore fans), sing songs of love of the club and then just go somewhere else. It would be absurd."
"I'm not interested in his brother's strategy," added the flamboyant club president. "The fact that Napoli have qualified for Europe seven years running, with dignity, is a clear indication that we are good enough."
"With us, Higuain has gone back to being what he was when he played for Real Madrid."
Despite his apparent hardline stance, Di Laurentiis said that Napoli, who were in Serie C when he took over the club in 2004, could survive without Higuain.
"I'm not really bothered," he added. "Napoli also finished second (in 2012/13) without him. We started in the third division and I'm proud of our club. I'm certain we will continue to do well."
(Reporting by Brian Homewood,; Editing by Neville Dalton)
