The Napoli striker has long been linked with a move to the Etihad Stadium, with his consistency in Serie A marking him out as one of the deadliest frontmen in European football.
There are, however, a number of obstacles City will need to overcome if they are to put a deal in place for Cavani.
The Uruguay international has a sizeable release clause in his contract and is also wanted by the likes of Chelsea and Real Madrid - clubs capable of competing with City financially.
Gregucci has, however, told a Naples-based radio station: "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.
"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."
City are in the market for a new striker after agreeing to offload Mario Balotelli to AC Milan towards the end of the January transfer window.
Gregucci believes that deal will be beneficial to all concerned, with City set to make a profit on the £19million they paid Inter Milan for the fiery Italian back in 2010.
He added: "Manchester will take more than it cost, and we and Milan will both benefit, as we all know Mario can be devastating.
"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."
Source: Manchester City MAD