The Italy international has reportedly attracted attention from across Europe after a series of impressive displays for Juve in recent seasons.
Reports have suggested that he could leave Turin this summer, with Juventus facing a battle to secure Champions League qualification.
The 25-year-old's representative Davide Lippi claims both Manchester clubs have been monitoring the situation, but Chiellini's focus is currently on finishing fourth with Juve in Serie A.
Chiellini would then look to sign a contract extension with the Bianconeri to put an end to speculation about his future.
"The primary objective of Giorgio is fourth place in the standings to get into the Champions League," Lippi told calciomercato.it.
"But we also give a little thought to the renewal of his contract. We met once with the club and I hope there will be another appointment soon.
"The intention is to remain at a great and glorious club like Juventus. We hope to find an agreement before the World Cup.
"Manchester City and United? Not only English but also some Spanish clubs would like to have Giorgio.
"In any case, his will is clear. He will stay quiet and continue to fight for the objectives of Juventus."
Source: Team Talk
Source: Team Talk