Part of the 50,000sq ft development could be taken over by staff from The Ministry of Housing, Communities & Local Government (MHCLG), which is expected to move to the West Midlands.
Around 1,000 staff are expected to relocate to the region, with 300 set for Wolverhampton and the rest based in Coventry and at a main hub Birmingham.
The i9 development near the railway station is due to open next summer.
Talks are understood to be at an advanced stage with one business over roughly half of the site, with bosses touting the rest of the plot as an ideal home for the MHCLG.
Councillor Ian Brookfield, said: "We welcome any investment in Wolverhampton. We have laid down the infrastructure and any Government department would find a home here.
"And why wouldn't they want to come? We have excellent transport, excellent facilities and 'A' grade office space. It is a fantastic place to be."
Recent reports said Housing Secretary Robert Jenrick, who was born in Wolverhampton, was keen to relocate some of the MHCLG to the West Midlands as part of an effort to shift Government focus away from Westminster.
The move, which was initially put forward by Wolverhampton South West MP Stuart Anderson earlier this year, is expected to be formally announced in the coming days.
Speaking at the stronger city economy scrutiny panel last week, Richard Lawrence, the Wolverhampton's director of regeneration, said the i9 site was "very much generating interest".
He said the authority was talking to a number of potential tenants and that the situation was "very positive".
"I think we can be confident of securing some activity in that site before it is open," he said.
"We are engaging through our agent, and progressing a number of conversations which we are hopeful will lead to legal discussions and hopefully a pre-let before that building is completed next summer."