But Yeung wants to bring in Vico Hui, the current chief executive of his company Grandtop International Holdings, to fill the role.
Gold was offered the chance to stay with Blues in a vice-president capacity, but the 72-year-old turned it down.
Yeung's representative, Peter Pannu, told the Birmingham Mail: "We have a lot of respect for David Gold and the excellent job he has done for the football club.
"Unfortunately we couldn't offer him the position of chairman which is what he wanted. Vico Hui is to come in as chairman.
"Regrettably our offer to David Gold to become a vice-president has been turned down so we were not able to come to a suitable agreement."
Gold replaced Jack Wiseman as chairman in 1997 after taking control of City along with Sullivan four years earlier.