Donald Trump’s son-in-law explored the possibility of setting up a secret line of communication with Moscow, according to US media reports.
The senior White House aide has not commented on the latest reports.
Mr Kushner is understood to be under scrutiny by the FBI as part of its wider investigation into Russian links.
Reports in the US say investigators believe he has relevant information, but he is not necessarily suspected of a crime.
The most recent reports – which cited US officials as sources – said Mr Kushner had spoken with Moscow’s ambassador, Sergei Kisylak, about setting up a backchannel using Russian diplomatic facilities in America.
This could be used to discuss Syria and other policy issues.
According to both reports, Mr Trump’s first national security advisor Michael Flynn was present at the meeting, held at Trump Tower in New York.
The New York Times said the line was never established.
The Washington Post had already reported FBI investigators were focusing on meetings Mr Kushner held last year with Mr Kislyak, as well as a banker from Moscow, Sergei Gorkov.
General Flynn was forced to resign in February after it emerged that he had misled other administration officials about the extent of his contacts with Mr Kislyak.
US intelligence agencies believe Moscow tried to tip November’s presidential election in favour of Republican Mr Trump, who went on to beat Democratic rival Hillary Clinton.
But President Trump has described the Russia investigations as “the single greatest witch hunt of a politician in American history”.
Mr Kushner’s lawyer has previously said his client would co-operate with any inquiry.