The Uruguay international has scored an impressive 18 goals in 20 Serie A appearances this season, prompting interest from Arsenal and City among a host of top European clubs.
The 25-year-old has a £55m buy-out clause in his contract and the forward is believed to be interested in a move to the Premier League.
Arsène Wenger has already spoken of his admiration for Cavani, and Gregucci expects the defending Premier League champions to face fierce competition to land the former Palermo star.
“City will definitely have competition for Cavani, who is dominating the Italian league with his goals and sacrifices for the team and whose contract has a £55m buy-out clause,” the City coach told a Naples-based radio station.
“Edinson is scoring a huge number of goals this season, and it will be difficult for City to take him. The 10 biggest clubs in Europe all have Cavani in their sights.”
Gregucci also backed City’s decision to sell Italy international Mario Balotelli to AC Milan in a £19m deal last week, with the Citizens coach confident all parties will benefit from the deal.
“Manchester will take more than it cost, and we and Milan will both benefit, as we all know Mario can be devastating,” he added.
“Mario will also benefit because, away from the clutches of the British media, he will be able to concentrate more on football objectives.
“Staying close to his family, at a club like Milan, which he loves, could be his salvation, but at City with [Carlos] Tevez, [Sergio] Aguero and [Edin] Dzeko you can make a big impact in training and still be on the bench.”
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