Press Association Sport understands the club are in negotiations with the Argentinian, who has been linked with a £6million switch to the Barclays Premier League champions.
City are looking for a new understudy to first-choice goalkeeper Joe Hart after Costel Pantilimon was released at the end of last season.
Caballero, 32, has also been linked with Monaco and Barcelona but his previous experience of working with City boss Manuel Pellegrini at Malaga could be decisive.
Pellegrini previously signed the former Boca Juniors goalkeeper for the Andalucian club from Elche.
City's interest in Caballero comes in spite of recent statements from Malaga president Abdullah Al Thani voicing determination to keep the player.
Al Thani, also responding to reports he could sell the club, wrote on Twitter: "Malaga CF is NOT for sale
Second, regarding Willy Caballero he is NOT for sale too.
"I am sure he's happy at Malaga CF
We didn't get any official letter from Manchester City to buy Willy.
"Me as a chairman of Malaga CF I would never let him go
He has been the best goalkeeper in those whole three years.
"I mentioned previously that we can't keep him if he wants to leave and the end it is his decision and I'm sure being with us will be his best decision, Malaga CF are his number 1 fans."
City, meanwhile, are understood to have no interest in Barcelona winger Alexis Sanchez.
Barcelona are reportedly prepared to let the Chile international - and compatriot of Pellegrini - leave the Nou Camp as they pursue a potential deal for Liverpool's Luis Suarez.
There have been suggestions of a potential swap deal for Suarez while Juventus, Arsenal and Manchester United have also emerged as possible destinations for Sanchez.
City are another club to have been linked with a big-money move but they are not preparing a bid.
City are limited to a net £49million spend this summer as punishment for breaching the Financial Fair Play rules of European governing body UEFA.
They have already made two signings after the £12million capture of midfielder Fernando from Porto and the free transfer of right-back Bacary Sagna from Arsenal.
City's non-World Cup players were due to report to Carrington for the start of pre-season training on Monday.
Source : PA
Source: PA