The club president has admitted that there has been contact with the Premier League side over both strikers and also responded to reports linking the club with Rafa Benitez.
The Premier League giant is keen to lure Cavani away from his current club, but has yet to table a concrete offer for the Uruguay international.
Napoli, on the other hand, sees Dzeko as a good alternative to Cavani in case the latter leaves this summer and De Laurentiis decided to contact City when he visited London on Monday to open talks over both strikers.
"I was in London to prepare for the European release of the movie on Steve Jobs. And then I told [sporting director Riccardo] Bigon to get in touch with Manchester City to open talks about Dzeko and see what their plans are with Cavani," the Napoli president told reporters.
"There's a lot of talk, but less action when it comes to actually spending money. Unlike me, others seem to be taking a lot of time to use their bank account."
De Laurentiis then went on to discuss the possibility of appointing Rafa Benitez as the club's new head coach following Walter Mazzarri's announcement that he will leave.
"I did not go to London for Benitez, but for my film commitments," he said. "I have heard a lot of names in the past six months as I knew Mazzarri would leave. The new coach will definitely be someone of Napoli's standard.
"I will have to make a decision on who will accompany me at this club in the years to come."
The Italian press claims that Benitez is in pole position for the Napoli job, while Roberto Di Matteo has also been linked with the Stadio San Paolo side.