In a radio interview in February, Racing president Victor Blanco announced a deal was in place for the 21-year-old to join the Premier League team in June.
And Racing revealed on Thursday that Zuculini, a former Argentina Under-20 international, has travelled to England in order to have a medical with City.
In a statement on their official website that offered details of a training session, Racing said: "The only player who was not present was Bruno Zuculini, who travelled to England to perform the medical examination at Manchester City."
Should Zuculini complete a move to the English champions, who confirmed the signing of Brazilian midfielder Fernando from Porto on Thursday, he would link up with several fellow Argentinians.
Sergio Aguero, Pablo Zabaleta and Martin Demichelis are already on the books at the Etihad Stadium.
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