A meeting this week between President Donald Trump's lawyers and the special counsel's office could be a flashpoint in the Russia probe.

The Washington Post reports that the president's team is shooting for a swift conclusion and special counsel Robert Mueller is gearing up for at least another year on the job.

The meeting is the first between the two sides since the completion of the special counsel's interviews with White House staff, according to CNN. It comes amid mounting criticism of the investigation from conservatives.

Attorneys for the president predicted publicly that the investigation into the White House would be over by Thanksgiving and have remained optimistic about a short timeline. That optimism isn't shared by those familiar with the probe, according to the Post. It said those sources told the paper that the probe could last well into next year.

While the president's team acknowledges that the investigation as a whole could stretch into 2018, they have advised the president that he will be cleared earlier, the Post said.

The president has expressed mounting frustration with the probe, even though he's certain he will not be charged with a crime stemming from Russia's meddling with the 2016 election.

"As we said, there's no collusion," Trump said, according to The Associated Press.

The White House declined to comment to CNBC on Tuesday. Ty Cobb, an attorney for the president, also declined to comment.

The meeting comes a week after among the special counsel's investigators.

"The Mueller team overwhelmingly ought to be attired with Democratic donkeys," Rep. Steve Chabot, R-Ohio, told the No. 2 Justice Department official.

On Friday, Rep. Jackie Speier, D-Calif., said there was a "rumor" that Trump was planning to fire Mueller. Trump denied that claim.

A spokesperson for the special counsel's office declined to comment.

Most special counsel investigations take years to complete, though Mueller's probe is moving faster than previous inquiries, according to an analysis from the website FiveThirtyEight.

Mueller's investigation has resulted in criminal charges against four Trump White House and campaign officials, including the guilty plea of former National Security Advisor Michael Flynn and the indictment of Trump campaign chair Paul Manafort on charges involving improper financial dealings. Manafort has pleaded not guilty, and is contesting the charges.

Read the full report from The Washington Post here.