The 19-year-old claimed he was subjected to the abuse during the City elite development squad's friendly against HNK Rijeka last Tuesday.
Croatia's Football Federation confirmed on Thursday it will be looking into the allegations and FIFA has contacted both it and the Football Association to ascertain more facts.
"We are aware of the incident," said a FIFA spokesman. "In this respect we are in contact with the relevant member associations to enquire and monitor the situation.
"We will be in a position to further evaluate the matter, once we gather all the relevant information.
"Generally speaking, FIFA takes a firm, zero-tolerance stance against any form of discrimination and racism and this is enshrined in the FIFA Statutes in article 3 which stipulates that 'Discrimination of any kind against a country, private person or group of people on account of race, skin colour, ethnic, national or social origin, gender, language, religion, political opinion or any other opinion, wealth, birth or any other status, sexual orientation or any other reason is strictly prohibited and punishable by suspension or expulsion'.
"This is further developed in the FIFA Disciplinary Code and the FIFA Code of Ethics.
"There must be no space for racism in football but recent incidents show us that the fight is not over."