The partners said the project could later expand to two gigawatts, helping to meet strong projected growth in demand for electricity in New Zealand.
The project will be CIP's first investment in New Zealand, and follows the Super Fund's $208 million commitment to CIP's new Energy Transition Fund last year.
The two partners said they were in the early stages of project feasibility evaluation, which included wind resource measurement, designing detailed environmental impact assessments with the support of local communities and experts.
It would also examine industry potential and training needs for the Taranaki region and focus on measures to ensure any project could co-exist with other uses of the marine area.
They said the success of offshore wind in South Taranaki would need engaging and partnering with key stakeholders, including local iwi, businesses and communities.
They said they have had positive initial discussions.
Super Fund chief executive Matt Whineray said offshore wind energy had the potential to be an attractive commercial opportunity that aligned with its climate change investment strategy.
"We are in the unique position of being able to attract best-in-class global partners on infrastructure developments that create positive environmental and social outcomes while delivering financial returns for New Zealanders through the Fund," he said.
Whineray said the climate crisis was driving a global shift in how countries produced energy.
"We are focused on opportunities that allow us to apply our long-term investment capital to support this shift and the Fund's own public commitment to being net zero by 2050," he said.
"While this proposal is still at a very early, exploratory stage, we are confident it could help New Zealand's transition away from fossil fuels and towards home-grown clean energy."
CIP Partner Michael Hannibal said New Zealand had "world-class" offshore wind fundamentals, such as high average wind speeds and relatively shallow waters close to transmission infrastructure.
"The New Zealand Government's renewable energy ambitions will require strong partnerships to deliver large-scale clean energy projects over the coming decade. We can think of no better partner than the NZ Super Fund to help bring our expertise to New Zealand."
If the project proceeds with regulatory approvals, CIP and the Super Fund said they could deliver power by the end of the decade.