McGahn had told the special counsel's office that he did not think Trump's actions rose to the level of obstruction of justice, two people familiar with his interviews said.
The timing of the White House's request - which was made to McGahn's attorney William Burck through top White House lawyer Emmet Flood, according to the official - is unclear.
"Mr. McGahn's cooperation with Mr. Mueller played a key role in allowing the special counsel's investigators to paint a picture in their report of a president determined to use his power atop the executive branch to protect himself from the Russian Federation investigation", the Times wrote.
White House officials declined to comment. After that episode was revealed, the president asked Mr. McGahn to create a White House document falsely rebutting his account. "Mr. McGahn declined. His reluctance angered the president, who believed that Mr. McGahn showed disloyalty by telling investigators for the special counsel, Robert S. Mueller III, about Mr. Trump's attempts to maintain control over the Russian Federation investigation". "It was a request, professionally and cordially made".
McGahn attended a farewell ceremony for Deputy Attorney General Rosenstein at the Department of Justice on Thursday when he was asked if he is going to testify but he did not respond.
In February 2018, Trump pressured McGahn to deny a news report that the president had pressured him to help oust Mueller.
Following the release of Mueller's findings, Attorney General William Barr-who has been accused of acting as the president's personal lawyer as he refuses to comply with congressional oversight-decided not to charge Trump with obstruction of justice.
Flood's request to McGahn was not the first overture by the administration in pursuit of such a statement, according to The New York Times.
In the redacted report released later, Mueller indicated that the investigation into possible obstruction of justice could not clear Trump.