The Burton boss is the bookies' new favourite to succeed Lee Clark.
As detailed by betting website Oddschecker, Rowett leads the running to become the Blues' next manager, with odds of as low as 10/11.
Former Manchester United assistant Mike Phelan had previously been the bookies' favourite but has dropped to third in the running.
At the time of writing, Karl Robinson is second-favourite, with Birmingham City reportedly having approached the MK Dons for permission to talk to their manager about succeeding Clark at St Andrews.
His odds may soon drop, however, as the Dons are said to have rejected that approach.
Having moved up one place, former Burnley, Bolton and Wigan boss Owen Coyle is fourth-favourite to take up the Birmingham post.
But a new name has entered the top five in Mark Cooper, the current Swindon Town manager. Cooper has coached seven clubs over a managerial career that has so far lasted nine years. Notably, however, the majority of those sides have been in the lower leagues.
Clark was sacked by Birmingham after a 1-0 defeat to Bolton Wanderers, the latest in a long line of poor results.