The Argentine will fly into Manchester in the next 24 hours, having cut short his post-season holiday, to undergo a medical and is expected to sign a three-year deal with the Premier League champions.
Sources report City already has agreed a to 8 million euro fee with Malaga for the shot-stopper, who has made more than 100 Primera Division appearances for the Spanish side since signing from Elche in 2011.
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Hart was again called into question for his performances with England at the World Cup, while he was dropped by City boss Manuel Pellegrini during the 2013-14 campaign after a series of high-profile errors.
Caballero, who worked with Pellegrini during his time in charge of Malaga, has developed a reputation as one of the leading goalkeepers in Spain's top flight and was previously linked with Barcelona before the Catalans signed Claudio Bravo from Real Sociedad.
City already has been active in the summer transfer window, with Bacary Sagna having arrived on a free transfer from Arsenal, while defensive midfielder Fernando has also signed and Bruno Zuculini is set to be confirmed within the coming days.
Convincing Yaya Toure to stay is set to be Pellegrini's main objective, however, with the Ivorian set for crunch talks with the club over his future after he suggested that City did not allow him leave to visit his dying brother in the hospital.