That push came amid concerns over the investigation of possible collusion with Russia, the Wall Street Journal reported on Monday, citing people familiar with the matter. Those lawyers, the report said, were concerned that Kushner was the advisor closest to the president and had the most dealings with Russian officials and business people during the campaign.
The Journal added that Kushner has said there were four meetings, but that he initially omitted any contacts with foreign officials on his security clearance form. He later updating it multiple times to include more than 100 contacts.
While the legal team wasn't unanimous in wanting Kushner to step down, press aides to the legal team had drafted a statement to explain his departure, the report said, citing people familiar with the matter.
One person said Trump wasn't persuaded Kushner should step down, while John Dowd, who joined the legal team in June and has since taken charge, said he wasn't aware the proposal was taken to the president, according to the report.
The Journal said the legal team's chief at the time, Marc Kasowitz, said he never discussed it with the president's other lawyers or recommended it to Trump.
Representatives of the White House, Trump's legal team and Kasowitz didn't immediately respond to CNBC's emailed requests for comment, which were sent outside of normal U.S. office hours.
Kushner's legal representative referred CNBC's inquiry to the White House press office.