The Guinea international walked from the field of play on Tuesday after angrily kicking the ball into the crowd during his side's TIM Trophy game with Sassuolo - who will play in Serie A for the first time in their history in 2013-14.
The Italian Football Federation (FIGC) has since launched an internal probe into the incident.
And FIFA have moved to reiterate their stance on racist abuse following the latest scandal to hit the Italian game.
In a statement released to OMNISPORT, the governing body said: "FIFA is monitoring the situation and awaiting the result of the investigation launched by the Italian FA.
"FIFA’s position on the issue of racism is unequivocally clear: there is no place in football for racism or for any form of discrimination. This is clearly described in the FIFA Statutes."
However, while FIFA were quick to credit Constant for his refusal to play on, they stressed that more needs to be done to tackle the issue of racism in the long term.
"As stated by the FIFA president (Sepp Blatter) after the incident involving Kevin Prince Boateng in January, if a player walks off the pitch because he has been racially abused, it is a strong and courageous signal, but it cannot be the solution in the long term.
"We have to find other sustainable solutions to tackle the problem at its roots."
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