"Referee Andre Marriner was made aware of an allegation at the end of the fixture and has subsequently reported this to the FA," the FA said in a statement.
"The FA will now begin making enquiries into the matter."
Defender Evra told French television station Canal Plus: "There were [TV] cameras. You can see him telling me this one word at least 10 times. There is no room for this in 2011."
Liverpool were not immediately available for comment but local media reported the club had said Uruguay international Suarez "categorically denied" the allegation.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.