The Trinidad and Tobago international striker has been offered a new one year contract at St Andrews as his present contract is due to expire this summer and the Telegraph claims that John has decided to sign the new deal in preference to a move to Pride Park.
"Stern John was a player we were interested in and the quality of player we are looking to bring to the club," Derby's director of football Murdo Mackay told the newspaper.
"We spoke to him but he has decided to stay at Birmingham and we wish him well."