Jared Kushner is under the spotlight after reports say he had three undisclosed conversations last year with Russian ambassador Sergei Kislyak.
"We're not going to comment on Jared," Trump's economic aid Gary Cohen said at a press conference in Italy.
Kushner is also a part of a federal investigation into Trump associates allegedly colluding with Russia during the 2016 presidential campaign.
Reuters first reported that Kushner made the three alleged phone calls to Russia.
The Washington Post also reported that Kislyak and Kushner discussed setting up a secret communications channel between the Kremlin and the Trump transition team.
During a press conference with Cohen on Saturday, National Security Adviser H.R. McMaster declined to speak about Kushner, but acknowledged that the US has back-channel communications with various countries that allow officials to talk in a discreet manner.
An attorney for Kushner responded late Friday about the alleged conversations with Kislyak and said that Kushner had many calls during that time, but doesn't recall those being alleged.
"Mr. Kushner participated in thousands of calls in this time period," attorney Jamie Gorelick said. "He has no recollection of the calls as described."
Two of the alleged calls took place between April and November last year.
Kushner's legal counsel said that he was part of the FBI investigation, but not a target.
His lawyer says Kushner will talk to federal investigators and Congress about his contacts and his role in the Trump campaign.