A company spokesman, Adam Sedo, reached by phone in Seattle said that Amazon would not comment on "rumours and speculation."
An update from the company is widely expected soon.
The Wall Street Journal said the main reason for having the two new facilities is to be able to recruit enough talent. Dividing the 50,000 employees expected to staff the headquarters between two locations also would relieve pressures from demand for housing and transportation.
The newspapers cited unnamed people familiar with the matter.
The New York Times said Amazon executives met last month with New York Gov. Andrew Cuomo and the state had offered possibly hundreds of millions of dollars' worth of subsidies. They also met with New York City Mayor Bill de Blasio, it said.
"I'll change my name to Amazon Cuomo if that's what it takes," the report cited Cuomo as saying.
Amazon's decision to set up another headquarters set off an intense competition to win the company and its promise of 50,000 new jobs. Some locations sought to stand out with stunts, but Amazon emphasized it wanted dollars and cents incentives, like tax breaks and grants. It also wanted a city with more than 1 million people, an airport within 45 minutes away, direct access to mass transit and room to expand.
Amazon has said it could spend more than $5 billion on the new headquarters over the next 17 years, about matching the size of its current home in Seattle, which has 33 buildings, 23 restaurants and 40,000 employees.