City, along with Premier League rivals Chelsea and Spanish giants Real Madrid, were heavily linked with a move for Cavani before he sealed a £55million transfer to PSG on Tuesday.
De Laurentiis has revealed that both Real and Manchester City made enquiries to sign the Uruguayan but baulked at the fee, while Chelsea never made a bid.
He also confirmed that new Napoli coach Rafa Benitez was keen on snapping up City striker Edin Dzeko, who has since by told by new boss Manuel Pellegrini that he is not for sale.
"Benitez very much liked Dzeko," De Laurentiis told Il Mattino. "Manchester City wanted to take Cavani but they never arrived at a certain fee.
"He [Cavani] had already asked to go away last summer but then we found the agreement to extend his contract until 2017.
"In these cases you put in the buy-out clause hoping that no-one will pay it.
"Real Madrid refused immediately to pay this fee, the same for City, while Chelsea never came forward."
De Laurentiis also revealed the lengths he went to in his attempts to find Cavani's replacement, confirming he had made enquiries about Borussia Dortmund's Robert Lewandowski, Fiorentina newboy Mario Gomez and unsettled Liverpool striker Luis Suarez.
However, new boss Benitez is keen on Real Madrid's Gonzalo Higuain and Internacional forward Leandro Damiao, with the Serie A side reported to be in transfer talks with both players.
"I contacted Lewandowski too, but he was already sold to Bayern Munich," he added. "I also contacted Luis Suarez and I made an attempt for Mario Gomez, calling [Bayern chief executive Karl-Heinz] Rummenigge on the phone who told me there was not yet an agreement from Fiorentina.
"But then I quit all of them because Benitez had other ideas."