The abuse is alleged to have been directed towards travelling Chelsea fans at Goodison Park.
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The Toffees moved out of the relegation zone in Duncan Ferguson’s first game in temporary charge, following the sacking of manager Marco Silva on Friday, thanks to goals from Richarlison and Dominic Calvert-Lewin (2).
However, the result has threatened to be overshadowed by news of the alleged homophobic abuse.
A club statement read: “Everton is working in conjunction with Kick It Out and has commenced an investigation into homophobic chanting reported during Saturday’s Premier League game against Chelsea.
“Both the club and Kick It Out have received reports of a homophobic chant being aimed at Chelsea’s fans by a small section of the home crowd.