The impeachment trial of U.S. President Donald Trump will likely begin Jan. 21, Senate Majority Leader Mitch McConnell said Tuesday.

Addressing reporters at the Capitol building, McConnell, who will hold the reins on the process after the House of Representatives transmits Trump's impeachment articles to the Senate, said he believes the trial will begin Tuesday when senators vote on rules that will govern the proceedings.

"That will come up appropriately next Tuesday, and that's when the vote would occur," McConnell said.

Before the trial formally begins the Senate will have to take care of housekeeping items, including swearing in senators as jurors, which will likely be done this week.

House Speaker Nancy Pelosi privately told House Democrats earlier Tuesday that the vote to transmit Trump's two impeachment articles will be held Wednesday. The House will also vote on naming lawmakers who will prosecute the trial in the Senate, known as "managers," Pelosi said during a closed-door meeting, according to reports citing anonymous Democratic sources.

The vote Wednesday will bring to an end a near month-long spat between Pelosi and McConnell regarding the transmission of the articles.

Pelosi has been withholding them since December in a bid to ramp up pressure on MCConnell as Pelosi sought to win concessions on the rules of Trump's trial, and whether witnesses would be called. But McConnell has held firm, refusing to budge on any matters before they are sent.

The Senate has yet to vote on the rules of the trial, but Trump is almost certain to be acquitted in the Republican-held chamber. Democrats would need 67 votes to remove him from office, but none of the Senate's 53 Republicans have indicated they would support Trump's removal.

Trump was impeached in December when the House approved abuse of power and obstruction of Congress articles against him.

They are tied to Trump's multiple requests to Ukraine to publicly declare criminal probes into Democratic front-runner Joe Biden, as well as his refusal to cooperate with the House's proceedings and his directive that top officials toe the same line.

Trump has dismissed the case against him as a hoax fabricated by Democrats, and called on his Republican allies in Congress to move for a quick dismissal of the case.

But McConnell said there is "little or no sentiment in the Republican conference for" that course of action, bucking the president's request and setting the stage for a longer-term process.

Chief Justice John Roberts will preside over the proceedings, which will see Trump become only the third president in U.S. history to face a Senate trial.