Juventus will also be worried over getting the 33-year-old fit for their Champions League quarter-final against Real Madrid with the first leg April 3.
Chiellini and his defensive partners provided a defending masterclass in their recent last-16 Champions League victory over Tottenham.
Italy play Argentina at Manchester City’s Etihad Stadium March 23 and England at Wembley March 27.
Interim Italy coach Luigi Di Biagio has called up West Ham’s Angelo Ogbonna to replace Chiellini.
