Speculation emerged last year that the state-owned Beijing Capital was exploring a sale.
Beijing Capital had asked investment banks for proposals on the potential divestment of the company, now called Beijing Capital Waste Management NZ Ltd.
New Zealand fund managers would welcome a return of the once highly profitable Waste Management, which delisted in 2006 after its amalgamation with Australia's Transpacific Industries.
Beijing Capital acquired Waste Management for $950 million from ASX-listed Transpacific in 2014.
It was the first major international foray for the Chinese water treatment, waste management, mass transit railway, toll road and property company.
The prospective deal is riding on the momentum of an industry that offers strong cash flows and rising public awareness of waste recycling.
Waste Management 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 a day.
Chinese companies dominate New Zealand's waste management sector.
The other main player is Envirowaste, which is owned by Hong Kong-based Cheung Kong Infrastructure Holdings.
KKR - formerly known as Kohlberg Kravis Roberts & Co - is an American global investment company that manages multiple alternative asset classes, including private equity, energy, infrastructure, real estate, credit, and hedge funds.