However, their hopes hang on a business case which Waterfront Auckland, the ministry, and Auckland Tourism, Events and Economic Development will finish in March.
Potential investors and tenants are being approached.
Officials said it was too early to say whether demand for such a facility was proven.
The extent of improvements needed on the industrial-style protected character building would also be assessed.
Mayor Brown said he was confident that a sufficient number of businesses wanted to move to the precinct and that the Government was committed to make it happen.
"The academic and business sectors have been screaming out for this approach for many years."
Dr Mapp said he, too, was confident of a positive business case verdict and foresaw the Lysaght building buzzing with undergraduates of Auckland's tertiary institutions.
"It ties in with other high-tech industry support, such as the IT entrepreneurial scheme, our commercialisation initiatives, and the range of business grants such as Tech NZ."
Mr Brown said the precinct would focus on adding value to the high-tech sector, notably information communications technology, digital content creation and marine technology. It would help Auckland to be a vibrant economy by producing exports that the country's trading partners wanted.
It would draw talented Aucklanders who otherwise would work overseas.
Mr Brown said he had held 16 meetings with export sector leaders and the need to set up clusters of related firms kept coming up.
The council also needs to ensure its investment in Wynyard Quarter, which opened in August, keeps attracting people and investors.
AIMING HIGH
Wynyard Innovation Precinct
* Campus-style high-tech project.
* Partnership between Government, Auckland Council and business.
* Centred on John Lysaght building, Halsey St.
* Whole 2ha block could be involved.
* Business case expected in March next year.