The towering centre-half, who is currently representing his country at the World Cup finals in South Africa, is being touted as a replacement for the Red Devil's defender Nemanja Vidic, who may decide to seek pastures new after the World Cup.
A host of top European clubs have bee linked with the Serbian defender, but United would be unlikely to allow their star man at the back to leave easily.
United's defensive frailties were exposed last season when a string of injuries saw them fall behind in the Premier League title race, and it appears manager Sir Alex Ferguson is wary of a repeat after already signing young Fulham defender Chris Smalling in January.
Davide Lippi, son of Azzurri boss Marcello and Chiellini's agent, said in The Sun: "United is a club and England is a country of great importance to us. We like them a lot.
"With Giorgio, we've decided that during the World Cup we won't think about the transfer market. But after the World Cup, we will think about everything. He is honoured to be of interest to United."
Chiellini, 25, is growing tired of the Turin club not offering him an improved deal.
His current contract at Juventus may also be appealing to Manchester United as the Italian earns just £1.7 million-a-year compared to Vidic's £4m annual salary.
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