Chalobah, on loan from Chelsea, alleged that he was subject to abuse during Forest's Championship draw against Millwall at The New Den on Tuesday.
The 18-year-old told the Forest's deputy manager of the incident at half-time, having supposedly heard the abuse initially early in the game when receiving treatment for an injury.
The FA has started investigating the matter, which has involved discussions with both Forest and Millwall.
An FA spokesperson told Perform: "The FA can confirm that we're speaking with both clubs for their observations and liaising with Kick It Out and the police on this matter."
Chalobah joined Forest on loan in September, having previously played in the Championship with Watford.
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