The News of the World says City are plotting a summer swoop for Higuain after a midweek mission to watch him in action for Argentina.
City's undercover scouts sent a glowing report back to the club after his stunning strike beat Germany.
Higuain is at the centre of a contract dispute with Real officials after turning down their latest offer of an improved deal.
The striker has scored 16 goals in 18 La Liga appearances this season and is considered to be one of the best strikers in Spain.
Higuain wants to stay at the Bernabeu, but believes he should be paid the same salary as French flop Karim Benzema.