The picture, published in more than one national newspaper, seems to show a fan making a 'monkey' gesture towards a United player during Wednesday night's Capital One Cup clash between the two clubs at Stamford Bridge.
Police are also aware of the photograph but have not yet received a formal allegation on which to open a criminal investigation.
A statement from the club read: "Chelsea Football Club can confirm we are investigating an incident involving a member of the crowd at last night's game against Manchester United.
"The club will be examining all available footage and asks anyone who can identify the individual to contact the club.
"Chelsea FC is committed to removing all forms of discrimination and if we have sufficient evidence we will take the strongest possible action, including supporting criminal prosecution."
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
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The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
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