Anthonia Onuoha, who acts as her son's agent, had emailed Cook saying that while she was "ravaged with cancer" it would not stop her negotiating on the player's behalf over a contract dispute he was having.
She received a reply, which seemed to be intended for the club's football administrator Brian Marwood, saying; "Brian... Ravaged with it!!...I don't know how you sleep at night. You used to be such a nice man when I worked with you at Nike. G"
Local media have reported that Cook has denied sending the email and said that his account must have been hacked.
"Following allegations made to the football club by Dr Anthonia Onuoha, subsequently reported in today's media, the club can confirm that a board led review has been launched into the matter," City said in a statement on their website.
Onuoha, 24, joined City in 2004 and spent last season on loan at Sunderland. The Nigerian-born player has represented England at Under-21 level.
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