Chiellini has been linked with a £25million move to Old Trafford as a possible replacement for Nemanja Vidic, should the Serbian depart.
The 25-year-old's agent Davide Lippi is quoted as saying in The Sun: "United is a club and England is a country of great importance to us. We like them a lot.
Lippi added: "He has a contract with Juventus but, given he's 25 and when he signed his contract he was very young, now is the time a player at his level has to get the contract a top player deserves.
"At Juventus, many have top contracts — but not Giorgio. "