Malaga, with their new-found riches, Manchester United and Manchester City are also understood to be attempting to sign the playmaker in an ongoing transfer saga.
Napoli have shown interest in Pastore, but Zamparini has dismissed reports that their Serie A rivals have made an new enquiry.
Zamparini instead believes that Chelsea or Real are the most likely destination for the 22-year-old Argentine.
"At the moment it looks as if Pastore will move abroad. Real Madrid and Chelsea lead the race for his services," he is quoted as saying by La Gazzetta dello Sport.
"There is not much news, as the same clubs still want him.
"Napoli have not made a fresh approach for him. Those quotes are outdated. They're from a meeting several weeks ago.
"(Napoli president Aurelio) De Laurentiis sat next to me and asked whether we could talk about Pastore. I said, 'no' and haven't heard from him since."
Source: Team Talk
Source: Team Talk