The Times, citing three people with knowledge of the discussions, reported that the topic was broached last year by Trump's lawyer John Dowd in talks with lawyers for former national security advisor Michael Flynn and former Trump campaign chief Paul Manafort.
Both men were charged with crimes as part of special counsel Robert Mueller's investigation of potential links between the Trump campaign and Russia. Trump has regularly denied any collusion between his campaign and Russia, and some of his recent statements have raised concerns that he is preparing to fire Mueller.
Asked about the president's views on his power to pardon at a White House briefing on Wednesday, press secretary Sarah Huckabee Sanders said, "There would be no reason for me to have had a conversation with the president about that, because that is not being currently discussed at the White House."
But Dowd reportedly raised the prospect of pardoning the two former officials last summer, shortly after he joined Trump's legal team, the Times reported.
Dowd reportedly told Flynn's lawyer that Trump was prepared to pardon Flynn on the basis that he believed the case against his former top advisor was flimsy.
Flynn pleaded guilty to making false statements to investigators about contacts with Russian ambassador Sergey Kislyak. Manafort, however, pleaded not guilty to dozens of counts levied against him in multiple indictments.
In a statement to NBC News, White House lawyer Ty Cobb said, "I have only been asked about pardons by the press and have routinely responded on the record that no pardons are under discussion or under consideration at the White House."
Cobb did not immediately respond to CNBC when asked if he was aware of Dowd's conversations at the time.
The special counsel's office declined to comment on the newspaper's report. Dowd did not immediately respond to CNBC's request for comment.