It is understood Cook denies sending the email, which was supposed to be going to City's director of football Brian Marwood anyway, and thinks his email account was hacked into.
"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," said a City statement released on Monday evening.
The claims relate to correspondence involving Onuoha's mother, who looks after all the player's contractual arrangements and Marwood over a dispute in October last year.
She was stunned to receive an e-mail, purporting to be from Cook, which mocked her use of the phrase "ravaged with it" to describe her condition.
"When I opened up my e-mails and saw the message, it was the worst day of my life, even worse than being diagnosed with cancer," Dr Onuoha told The Sun.
"I couldn't understand how anyone could behave like that. I'm critically ill.
"I cried and cried for hours."
Source: PA
Source: PA