It would be built along with the 165-room hotel on the site in Cable Street.
The overall project would be financed by local developer Mark Dunajtschik.
"We'll be asking councillors to vote to take the proposal out for consultation," Ms Wade-Brown said.
"Our facilities, while individually attractive and good for boutique events, are too small and, in some cases, too old, and lacking the flexibility needed for the modern convention market."
Deputy Mayor and Governance, Finance and Planning Committee chairman Justin Lester said the proposal was a cost-effective way to secure a large and modern convention facility with little risk to ratepayers.
"The Council is working with a leading local developer prepared to invest all the capital and carry most of the risk - for our part, the city would lease the new convention centre and the Hilton hotel chain would run it."
If the Council votes next week to support the proposal, a formal consultation period would run from July 8 to August 8 and a final decision would be made in September.
If the proposal is voted in
* estimated to grow the overall business in Wellington by about 10 per cent ? about 74 new events delivering 68,000 delegate days each year;
* that growth would add $30 million in new expenditure and directly create more than 200 new jobs;
* net cost to the city would be $2 million a year over 10 years;
By the numbers
* 165-bed 5-star hotel and purpose-built conference facility with full-format conference hosting capacity of up to 1200 delegates and banqueting capacity for up to 1450 people;
* in theatre style seating, the facility can seat 2500 in the largest space; and
* at the time of completion, the new venue would be the second-largest convention facility in the country.