Despite reinstating Joe Hart as his number one after an early season first-team exile for the England international, the Sky Blues chief is rumoured to remain unhappy with his current options between the posts.
A deal for Barcelona’s Victor Valdes was believed to be the preferred solution to Pellegrini’s worries, but the Spaniard has since been ruled out for an extended period of time with a serious knee injury.
With his recovery time and potential to get back to his best unclear, Caballero has now emerged as an option.
Pellegrini coached the Argentine while at Malaga, and is known to be a big fan of the stopper.
The Spanish club will be against the idea of losing their man, but with a £20m release clause in his contract, City could force through a swoop in the coming months.
The 32-year-old has bags of experience having represented Boca Junior in his homeland as well as Elche and Malaga.
Pellegrini is known to be open to signing previously coached players, with Martin Demichelis another star he worked with at La Rosaleda.