The Sun says the 64-year-old wasted little time getting back into management after his departure from the Etihad last year.
He is currently in charge of Chinese Super League club Hebei Fortune.
However, the experienced chief has shot to the top of his country’s wanted list as they begin the search for a new leader.
Juan Antonio Pizzi quit his job this week following the team’s failure to qualify for the World Cup finals.
Pellegrini, who managed City to a Premier League title and to two League Cup triumphs, is a close ally of Chile FA president Arturo Salah.