Re-elected Wairoa councillor Mr Wilson has remained tight-lipped on whether he would seek the role again. He had been speaking with others to "get the best way forward for a new mix of councillors".
"It'll be a suprise for everyone," he said yesterday, "we'll go through the process tomorrow."
Central Hawke's Bay councillor Debbie Hewitt said she "would certainly hope the newly elected chairman is prepared to be impartial, and is ready to represent the best interests of all of Hawke's Bay".
Yesterday evening, Hastings councillor Tom Belford said it would be a "smart bet to bet that Rex Graham will be chairman by this time tomorrow".
"The new chairman ... will have a lot to do with the tone and culture at council," he said.
"An important change could occur tomorrow."
Ngaruroro ward councillor Peter Beaven said he would be supporting Mr Graham, and it was his expectation Mr Graham would receive enough support from councillors to win the role.
New Napier councillor Paul Bailey - touted as changing the council majority - said he would be voting for the best person for the role, "regardless of where they come from".
Hawke's Bay Today understands Hastings councillor Rick Barker and returning Napier councillor Neil Kirton could be suggested for deputy chair.
Mr Kirton said he hoped to chair a committee, but would leave the chairman and deputy chairman role to others, although he added "we'll see on the day".
Mr Barker said people had told him they would nominate, and second him as deputy chair. He would not say who they were.
Napier councillor Alan Dick could not be reached for comment.
Other items on today's agenda include fixing the date of the first ordinary council meeting, and appointing a proxy and alternate to vote on council's behalf at the fifth Annual General Meeting of Hawke's Bay Regional Investment Company Limited (HBRIC Ltd) in November.