At a meeting at Trump's Mar-a-Lago resort in March 2017, the president berated Sessions for recusing himself and asked him to change his mind, saying he needed a loyalist overseeing the investigation, the Times reported. Sessions refused, the article said.
A representative for the attorney general did not immediately respond to CNBC's request for comment. The special counsel's office declined to comment, and the White House referred inquiries to the president's outside counsel.
Later Wednesday morning, Trump tweeted that he wished he had picked another person to be attorney general.
Rudy Giuliani, one of Trump's attorneys in the Russia probe, told CNBC that Trump still seems frustrated over Sessions for the recusal "because he believes he should not have in the first place."
Ever since Sessions recused himself from the Russia investigation, Trump has attacked sessions both in public and in private. The president has frequently taken to Twitter to slam Sessions.
The Times, citing a source, also reported that Trump, in July, had told his chief of staff, Reince Priebus, to convince Sessions to resign. Priebus then informed the attorney general's chief of staff, who told Priebus that the president himself would have to ask Sessions to quit, which did not end up happening, the report said.
Priebus was out as chief of staff by the end of July, replaced by John Kelly. The Times reported that Mueller's team wants to ask Trump about his discussions with Priebus regarding Sessions.
Read the full report in The New York Times.
CNBC's Brian Schwartz contributed to this article.