The Napoli striker has become one of the hottest talents in European football in recent years, and according to the defensive coach, Roberto Mancini is keen on bolstering his side by adding the Uruguayan hitman to his squad.
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"Mancini decides the transfer targets along with the new directors. If you ask the clubs who can afford Cavani, for example Real Madrid, Bayern Munich and Manchester United, then I think they'd want Cavani just as Manchester City want him.
"However, what the player wants is the predominant factor in negotiations and it seems to me that Cavani is happy at Napoli."
Gregucci also praised striker Mario Balotelli, who was involved in a well publicised training ground bust-up with Mancini. Despite the incident, Gregucci says the 22-year-old is "a treasure", and stated that he is one of the top 10 strikers in the world.
He added: "Mario has huge potential and is a treasure for our football. As for the recent events, I'd prefer not to talk about them so as not to make too much of it.
"Seeing him train, though, I think Mario should be included in the world's top 10 strikers."