James is looking for a move away from Santiago Bernabeu after his two-year loan spell at the Allianz Arena ended with Bayern opting not to trigger a clause to sign him permanently for €42 million (£37m/$47m).
A move to Napoli has been widely tipped, although the playmaker admitted last month that Real Madrid will have a significant influence on where he ends up next season.
And De Laurentiis says Napoli are waiting to come to terms with the Liga club.
"James is the footballer who, after Cristiano Ronaldo and Messi, is considered one of the best," De Laurentiis told Corriere dello Sport.
"Ancelotti likes him very much, and James wants a move to Napoli, but we are waiting for a more reasonable demand from Real. They have high demands in our opinion."
On those rumours, De Laurentiis added: "He [Rodrigo] prefers to stay there [at Valencia]. He told us and we take note of it.
"With Elmas, at that age you are no longer a kid. We have a lot of interest, I can't deny it, but it is necessary that we complete some departures to avoid the overcrowding that, as you know, is never productive.
"Icardi has always wanted to go to Juventus. But I also prefer Lorenzo [Insigne], because we need him, while in front of him we have [Arkadiusz] Milik and [Dries] Mertens."
There have been some high-profile managerial changes in Serie A over the summer, with former Napoli boss Maurizio Sarri having returned to take charge of Juventus and Antonio Conte moving to Inter.
Conte has said he is keen to close the gap to Juve and Napoli, who have finished first and second respectively in three of the last four seasons.
"Conte, to whom I welcome back, knows Italian football and has remained connected during his mission in England," De Laurentiis continued.
"He noted our progress, that of a club that has been permanently in Europe for 10 years. I would like to add that our willingness to improve ourselves, which has been indisputable in the past, remains the same for the future as well: it will be a wonderful championship, with six or seven teams closer together, and therefore a year will come in which there is more interest and intrigue."