The 26-year-old has been without a club since leaving MK Dons but Blues boss Gary Roweet could offer him a contract to ease his defensive worries.
Spence came through the ranks at West Ham but left in 2014 having made seven Premier League appearances for the club.
Since leaving east London permanently he has made 71 league appearances for the Dons before his release at the end of last season.
Spence has been training with Rotherham recently and looked set to sign a deal with them but he could now be headed for a permanent contract at Birmingham instead.