The Serie A side are keen to tie up a deal for the Spaniard and the two clubs are currently in dialogue over a switch for the 28-year-old.
Michu has not travelled with the rest of the Swans squad as they left for their pre-season tour of the United States, and De Laurentiis explained that talks between the two teams have been in the pipeline for a number of weeks.
The BBC quotes him as saying: "Michu? Negotiations are well under way for months but there is still no agreement reached."
De Laurentiis believes that the deal will eventually come to fruition next month, and Michu looks likely to join Rafael Benitez's side for next season.
The Italian was also quoted as saying by Calcionews.com: "Some situations will begin to unlock in the first few days of August. We are not only looking for the name, but a profile that is useful to the team and the coach."
Michu has been a big success since his £2.5 million move from Rayo Vallecano in 2012, and after converting to a traditional centre-forward with the Welsh side, he finished as the club's top scorer in his debut campaign with 22 goals.
Michu's displays saw Arsenal and Liverpool linked with a big-money move, before he inked a four-year deal with the Swans in 2013.
A knee injury, coupled with Wilfried Bony's continued selection up front caused Michu to churn out a less productive season last term, although he did win his first cap for Spain in October 2013.
Michu could only manage two goals last season in 15 appearances, and former Swansea winger Leighton James has called for a swift resolution to the transfer saga.
He said: "If he's going to go, then get it sorted. Even before he was injured last season he was giving out the impression that he didn't want to be here.
"His price has dropped drastically through his poor form last season and his long-term injury. So you can't expect to command the same sort of fee that you could have done 12 months ago after he had such a good season."