The Mail on Sunday says the 32-year-old is well thought of by manager Manuel Pellegrini and regarded as a strong character. City want competition for Joe Hart who has suffered an indifferent season so far which has drawn criticism in some quarters.
Argentine Caballero said: "I spoke to Pellegrini before he left Malaga. I know of his intention to take me with him but I was unsure whether he would stick with the goalkeepers he had or play me."
However, he is understood to be open to a move to Manchester as Malaga contemplate selling their highest earner in January.
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