If given the green light, the money will be used to repair the roof and electrics as well as refurbishing office space and toilet areas. The council says the work will open up capacity so the council house can be used more flexibly by more employees.
Money will also be used to improve security and replace the existing microphone system in the council chamber.
Plans to refurbish the building were first put to cabinet last year and have gone through a full scrutiny process since then.
Dudley Council was also recently awarded £4.4 million from the Government's public sector decarbonisation scheme. The cash will be used to make improvements to a number of council buildings across the borough, including the Grade II-listed council house campus – and plans will go before the authority's cabinet next week.
The aim is to switch council buildings across the borough to electrical forms of heating that will eventually become zero-carbon.
The grant includes funding to install air source heat pumps, solar photovoltaic and battery storage and LED lighting.
Councillor Simon Phipps, cabinet member for regeneration and enterprise, said: "The council house is a big building, which has stood proud in Dudley town centre for nearly 90 years. It’s home to the borough’s democracy and one of the most significant council buildings.
"It’s right that we look at ways to make the building more energy efficient in the long run, this will not only offer cost efficiencies but also contribute to our zero-carbon efforts.
"The building is also in need of extensive repairs to make it a suitable working environment for our staff, and I am pleased colleagues from all parties on the scrutiny committee support plans to invest in the building’s future.
"If we don’t carry out the works now, we know they will prove more costly in the long run."
The plans will go before cabinet on June 24.