Showing images of the Gucci store on Queen St near Louis Vuitton, the shared space on Darby St and Vulcan Lane, he told how Auckland's CBD had 247,000sq m of retail space yet a low vacancy of just 3.2 per cent.
Leasing specialists have said a rising number of Asian migrants and tourists was a big factor in new luxury brands arriving.
A spokesman for Mr Brown said the work was ongoing but didn't answer questions about which companies were being targeted and when they might arrive.
"The mayor is confident Prada won't be the last upscale international store to be attracted to Queen St, as he and the council continue to work towards lining up more well-known international retailers to Auckland.
"Initial discussions in Sydney in 2012, and other meetings during the past four years, have resulted in positive responses from premium brand retailers that are being followed up," the spokesman said.
Mr Beasleigh said it was no secret many big names were considering Auckland, some with their eye on the luxury shopping hub at the foot of Queen St.
"There have been a lot of brands over here, checking New Zealand out. Everyone's talking about Zara and Apple has been looking around for a while. Tiffany have been looking for years and they were quite close to taking where Dick Smith are on Queen St," he said, referring to the ground-floor of Zurich House fronting Queen Elizabeth II Square.
"The issue is do we actually have the properties that suit their requirements?" he asked, indicating high demand but short supply of Queen St retail space.
The long-vacant ground floor of 125 Queen St - which is the ex-BNZ Tower with New World Metro in its basement - was being eyed by a major retailer, he said.
Luxury brands with Australian offices were often the ones making decisions on whether to expand into New Zealand.
"Cartier were looking," he said, but they wanted to be in the same luxury retail zone as Gucci, Louis Vuitton, Swarovski, Prada and Christian Dior.
Asked about the financial feasibility of Auckland stores, Mr Beasleigh said one Hong Kong Louis Vuitton outlet turned over US$400 million ($517 million) a year. "So if they make $20 million a year down here, yeah, it's okay," he said.
JLL's Asia Pacific luxury and mid-tier brand monitor showed only Perth and Adelaide have fewer outlets than Auckland.
Top shops
Prada: Opened this month, 45 Queen St.
Christian Dior: About to open alongside Prada.
Swarovski: In same building, has just opened.
Topshop: Opening opposite Whitcoulls on Queen St early next year.
*Mayor wants to bring in Apple, Tiffany and Google.