The initiative was announced by then-Labour leader Andrew Little in Dunedin in 2017.
The centre, called "Code" and to be paid for by the Provincial Growth Fund, would have $10million spent on it over 10 years, to build on the city's digital strengths.
A chair of computer gaming at the University of Otago would also be established, a gaming incubator launched and a funding pool made available to attract talent to the city.
Last month, it was reported the business case underpinning the bid for PGF funding was close to completion.
This week, Enterprise Dunedin economic development programme manager Fraser Liggett confirmed its case was expected to be submitted by the end of this month.
Enterprise Dunedin staff had been working with industry representatives - in New Zealand and overseas - to help shape the project.
Design workshops had been held with groups including the New Zealand Game Developers Association, Dunedin and international gaming companies, the University of Otago, Otago Polytechnic, secondary school representatives, Ministry of Business Innovation and Employment and Education New Zealand, he said.
The aim was to build a business "ecosystem" and grow the gaming industry around Code, by focusing on leadership, education, research and innovation, international connections, fostering local talent, diversity and inclusion, he said.
Code would also seek help the start-up companies in Dunedin, enabling them to scale up and build capability, he said.
As part of that, new links had also been fostered with gaming industry representatives based in England, Scotland and China, including Abertay University, in Dundee, and Capital Enterprise London, he said.
The aim was to support the "global export potential" of Dunedin's computer gaming sector "as well as gain access to potential investors and industry talent", he said.
Elsewhere, the DCC was expected to formally present the city's waterfront development project to a PGF panel in Wellington later this week.
A recommendation would then be sent to Cabinet for a final decision later this year.
A new city engineering hub, being promoted by Farra Engineering chief executive Gareth Evans, is also working on a feasibility study. Conclusions and recommendations were due in March.
Mr Evans could not be contacted for an update yesterday.
