Chiellini has had his head turned by the mounting interest and his representative has now revealed that he would be foolish not to listen to United were they to make a move.
Davide Lippi told Radio Radio: "Manchester United? It is a club of great importance and we particularly like that.
"With Giorgio we have decided not to talk about the market until after the World Cup, then we will reflect on everything."
"We are honoured to be at Juventus and to have attracted interest from clubs like United and Real.
"Giorgio signed a contract with Juventus two years ago, when he was young, and he has now enjoyed two great seasons and reached a top level.
"It is time for Chiellini to have the contract of a top player.
"We have talked of renewing, but not with the new board. They don't seem to be in any hurry to lock down a key man like Giorgio.
"For now everything is on hold, but we will see."