The 25-year-old has been heavily linked with a switch to the Premier League in the summer, but Gregucci has claimed that the English champions will face a fight to secure the signature of the highly-rated forward.
"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," Gregucci told a Naples radio station, according to the Manchester Evening News.
"Edinson is scoring a huge number of goals this season, and it will be difficult for City to take him. The ten biggest clubs in Europe all have Cavani in their sights."
City boss Roberto Mancini is expected to be in the hunt for a new striker at the end of the season following the sale of Mario Balotelli to AC Milan.