Work could start on it as early as this year depending on the sale of the existing building and negotiating an early termination deal with Eastside Tavern.
Remediation work on the existing 401 Grey St headquarters will begin next year but the council would begin to "discreetly" look for potential buyers if members agreed.
The upper floor of the main block was discovered to be leaky last year.
Options to be presented to the council include whether the build would begin this year or in three years' time and whether it would lease it back from a property firm or own it.
Sources have indicated there appears to be enough support within the council to sign off the development.
If approved, the project is likely to be included in the draft long-term plan budget which the public could then have their say on.
Leasing appeared to be the preferred option as the council would have to explore funding options if it were to take ownership.
The average cost to ratepayers would be 87 cents a year to lease it back and $1.30 a year to own it.
Council staff now work across four offices in Hamilton and projections that staff numbers could rise to 550 by 2023 have prompted the council to look for a larger premises.
Eastside Tavern owner Nick Field said he hadn't been approached by the council about the development or had any negotiations about exiting the lease early.
Mr Field said he was keen to keep running the bar until at least 2015 from the site which is the city's oldest licensed premises area.
"Obviously we would like to stay.
"We knew they bought the site for that reason and were close to making a decision."
The existing headquarters was built in 1994 to 1995 and includes senior management offices, the councillors' lounges and council chambers.