The 25-year-old centre-back has made more than 100 Serie A appearances for the Old Lady - scoring 11 times - since arriving from Fiorentina in 2005.
But with Cira Ferrara's side struggling in 2009/10, speculation has surfaced claiming the Italy international - capped 27 times by the Azzurri - is wanted by both the Red Devils and the Blues, who clashed on Wednesday night in the first leg of their League Cup semi-final at Eastlands.
Sir Alex Ferguson has seen his back-line decimated by injury this season, with Rio Ferdinand, Nemanja Vidic, Wes Brown, John O'Shea, Jonny Evans, Gary Neville, Fabio and Rafael all enduring spells on the sidelines.
While new City supremo Roberto Mancini is believed to be keen on adding Chiellini to his ranks with both Joleon Lescott and Wayne Bridge sidelined.
However, the defender's represenitive Davide Lippi is not convinced that a deal will be completed before the winter transfer window closes.
"The market is usually open all year and we are always speaking about things in Italy and England," he told Sky Sport Italia.
"Chiellini is an important player and when a player is important then it's obvious that he will interest teams.
"But he is a Juventus player and captained the team against Milan and so I don't think there is anything in this situation.
"It's not only Chiellini though. There could be other players that interest City and United."
