It was the first major international foray for the Chinese water treatment, waste management, mass transit railway, toll road and property company.
Bloomberg said deliberations were at an early stage and Beijing Capital could decide to keep the business.
Beijing Capital did not respond to requests for comment from the agency.
The prospective deal is riding on the momentum of an industry that offers strong cash flows and rising public awareness of waste recycling.
The waste management unit has five landfills in New Zealand and operates 29 refuse transfer stations and more than 800 specialised waste collection vehicles. It has more than 1200 employees and handles more than 8500 tonnes of waste per day.
Chinese investors dominate New Zealand's waste management sector.
Hong Kong-based Cheung Kong Infrastructure Holdings owns the other major player - Enviro (NZ), which operates as EnviroWaste.
According to its latest filing to the New Zealand Companies Office, Beijing Capital Waste Management turned in a $258,000 loss for calendar 2020, down from a $16.9m profit in the previous year.
Revenue came to $503.4m in 2020 from $519.7m a year earlier, while net financing expenses shot up to $79.6m from $67.2m.
Separately, Macquarie Group's infrastructure unit this month acquired Australian waste management firm Bingo Industries Ltd for about A$2.5b ($2.6b).
Beijing Enterprises Holdings has considered a sale of its overseas waste treatment unit for about US$2b, Bloomberg reported Wednesday.
In another waste deal, Platinum Equity agreed in June to buy Spanish waste management firm Urbaser SA from the Chinese environmental services group China Tianying Inc.