The film mogul wants a new ground on the San Paolo site and he told a radio station that if mayor Luigi de Magistris doesn't give him a price by Tuesday then he will make arrangements to build a new home 45 kilometres away in Caserta in January.
"I am very worried because the mayor said that he would sell me the San Paolo, but I do not think that with the biblical times with which the politicians handle things they will be able to tell me how much they want for it by Tuesday," he told the Kiss Kiss radio station.
"They will say that it will not be possible because of the city council and all sorts of other things.
"At that point I go to the mayor of Caserta, find an agreement with him, and from January 2 I will begin the construction of a new stadium away from the city, because they are serious. If de Magistris says he has no powers to do this one thing, then he should resign."
The Corriere Della Sera newspaper also reported de Laurentiis saying he will be leave Italy for the United States if he doesn't get what he wants from the city council.
"I've invested my own money in Napoli and I want to do serious things. If I have to stay in Naples I don't want to hear any more 'Italian' talk," he said, lamenting the slowness of bureaucratic procedure in Italy.
"Los Angeles is ready for me, it's my second home. I'll go there and you can get on with it yourselves in Naples and they'll all be happy and contented."
The issue of new stadia is a vexed one in Italy, where most clubs play at grounds owned by the local authorities.
The new Juventus Stadium has shown Serie A clubs how modern facilities can attract more fans and bring in more money, crucial in light in Uefa's Financial Fair Play regulations.
The Italian champions announced record revenues of 274.8 million euro ($372.12 million)earlier this week. ($1 = 0.7385 euros)