The FBI is now investigating Jared Kushner, President's Donald Trump's son-in-law, in the probe delving into the presumed links between the magnate's presidential campaign and Kremlin, according to US media reports on Thursday.

Kushner met during the campaign and the transition period with Russia's ambassador to Washington, Sergei Kislyak, and with banker Sergei Gorkov, the CEO of Vnesheconombank who studied at the Russian secret service academy.

According to the anonymous sources cited by The Washington Post, Kushner held a "series of meetings" with Russian operatives in December, during the transition period.

The husband of Ivanka Trump's meetings with Kislyak and Gorkov attracted the attention of investigators because of the "extent and nature of his interactions" with the Kremlin, The Post reported.

 According to NBC News, FBI investigators believe that Kushner has "significant information relevant to their inquiry," but the network added that "does not mean they suspect him of a crime or intend to charge him."

 The Post had reported last week that a top White House official close to Trump was being focused upon by the FBI in its probe, but at the time the paper did not say that Kushner was that person.

The White House has called the meetings Kushner had with Kislyak and Gorkov during the transition period routine, although he had also met with the envoy in April 2016 during the election campaign.

Kislyak held numerous meetings with retired Army Gen. Michael Flynn, who is also the focus of the FBI probe and who served briefly as Trump's national security adviser before being forced to resign amid the Russia scandal.

Jamie Gorelick, one of Kushner's attorneys, issued a statement on Thursday saying that he would cooperate with the investigation.

"Mr. Kushner previously volunteered to share with Congress what he knows about these meetings. He will do the same if he is contacted in connection with any other inquiry," Gorelick said.