The fact Bruce has not yet signed doesn't worry either of the club's owners however.
"Steve's on holiday in Barbados, but everything's been agreed and we will formalise things when he gets back," Sullivan told Sky Sports News.
"We have agreed a new five-year contract, even though he's still got two or three years on his current contract, although we've not put pen to paper.
"Steve's a gentleman. His handshake is as good as a signature on a contract as far as I'm concerned. I think he'll be at Birmingham for some time."
David Gold, interviewed by Sky Sports News at the opening of one of his Ann Summers shops in Solihull said: " We are not worried one iota that Bruce hasn't signed yet.
"He is the best manager we have worked with during our time at the club."