Carlo Tavecchio, the current FICG vice-president, has been considered among the front-runners to replace Giancarlo Abete - who resigned his position following Italy's exit at the group stage of this year's World Cup.
However, his bid has been hindered after he reportedly made reference to "banana eaters" in response to the influx of foreign players in Serie A at a meeting of Italy's amateur leagues.
And FIFA's task force against racism and discrimination, led by chairman Jeffrey Webb, has now written to the FIGC requesting that an internal inquiry be held.
"Media reports concerning alleged racist comments by one of the presidential candidates for the Italian FA have alerted FIFA’s task force against racism and discrimination and its chairman Jeffrey Webb," read a statement from FIFA.
"As such, FIFA has written a letter to the Italian FA asking it to take the appropriate steps to investigate and decide on this matter and report to FIFA.
"In the letter, FIFA reminded the Italian FA that the fight against racism is a top priority for FIFA.
"In 2013, the FIFA Congress unanimously passed a strong resolution on the fight against racism and discrimination, which, among other measures, reminded the member associations about their obligation to put every effort into eliminating racism and discrimination in football.
"In its correspondence, FIFA also stressed that officials of the football community are expected to act as role models in the fight against racism."
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