The Uruguay international is also a target for both Chelsea after notching 102 goals in 124 matches for the club in all competitions over three seasons, but Goal exclusively revealed a player-plus-cash deal involving Edin Dzeko has stalled.
De Laurentiis, while revealing Chelsea's interest, has always maintained Cavani will only be sold if his €63 million [£53.7m] buyout clause is met, and City has now seemingly ruled themselves out of the running after failing to lower the price tag.
|5/2||Edinson Cavani is 5/2 with Betvictor to join Manchester City
"I could accept a part-exchange deal if the players proposed are attached with a figure that represents the actual value of the player.
"[Edin] Dzeko for example, is no longer what he once was, he was not a starter last season. He did not perform how he did in the Bundesliga [with Wolfsburg]. This is assuming that Dzeko wants to join Napoli, of course."
De Laurentiis did, however, backtrack from his previous statement that Chelsea were interested in Cavani by claiming the Europa League winners are yet to make their interest concrete.
He added: "Chelsea never made contact with me. I have always heard rumors indirectly."
Cavani recently described a possible move to Real Madrid as a 'dream', but De Laurentiis says the striker's words were taken out of context, though admitted a move to Santiago Bernabeu would likely be hard to turn down.
"With Edinson nothing has changed," he said. "Headlines I've read in the papers did not represent his words exactly. He could never deny the importance of a club like Real Madrid's, but don't forget that he made his name at Napoli.
"If a club like Anzhi enquire about him, maybe he says no, but other clubs like Bayern, Barcelona or Real Madrid could persuade him to leave.
"He knows that he has a contract and an obligation to us, and there is a buyout clause. Cavani knows that at Napoli is he is the most important player. I do not know whether, at Real Madrid or in other teams, he will be as important.
"[Cavani] will decide what to do and we will support him."