Mancini has previously expressed an admiration for Cavani, who is regarded as one of the most potent forwards in world football.
Napoli have recently insisted it will cost £60million to persuade them to sell, although the Uruguay international said he is unsure where he will be playing next season.
Chelsea and Real Madrid are other clubs to have been linked with Cavani, and Gregucci says there is no 'exclusive' deal for City to sign the player.
"He is an important player and any club which wants to be better must look at players like him," Gregucci told Radio Crc.
"Mancini has expressed his appreciation for Cavani, but there is no 'exclusive' for City."
Reports have suggested that a deal for Cavani would prompt the summer departure of Edin Dzeko, but Gregucci would not be drawn on whether the Bosnian striker would be sold.
He added: "Dzeko is an important player too and, at the moment, it seems inappropriate to speak of the market."
City's faltering defence of their Premier League title has also raised questions over the future of Mancini at the Etihad Stadium.
Gregucci commented: "Mancini has a contract with City, we will see at the end of the season."