The Juventus centre-back, 25, is the Manchester United chief's top choice to replace Nemanja Vidic, should the Serb quit Old Trafford as expected.
Despite being one of the biggest names in Serie A, Chiellini earns a modest £1.7m a year and has two seasons left on his current contract at Juve.
It is understood that the Old Lady of Turin would accept a bid for him as they look to rebuild their side following a disastrous season - they finished seventh in the Italian top flight.
And Fergie is on red alert, with Manchester City expected to launch a £20m bid for wantaway Vidic in the next few days.