Trump adviser George Papadopoulos allegedly told Australia’s top UK diplomat that Moscow had incriminating “dirt” on Hillary Clinton.
The newspaper alleges the revelation came “during a night of heavy drinking” in London in May 2016.
Australia later informed the FBI.
The New York Times report claims that the exchange was the spark for establishing a secret investigation into possible connections between Russia and the Trump campaign in July 2016.
The newspaper’s story cites four anonymous American and Australian foreign officials “with direct knowledge of the Australian’s role” as its source.
The BBC has not independently verified the claims.
Mr Papadopoulos has already pleaded guilty to lying to the FBI about meetings arranged while he was working with the Trump campaign.
The FBI’s original investigation has since been handed off to special counsel Robert Mueller’s probe, with which Mr Papadopoulos is now cooperating.
The White House has attempted to portray him as a “low-level volunteer” with little influence within the campaign.
However, Mr Papadopoulos is known to have attended several meetings with Mr Trump and other senior officials such as Attorney General Jeff Sessions, as well as meeting a British foreign office official and arranging high-level meetings. (Courtesy BBC)