The House impeached Trump last month on charges of abuse of power over pushing Ukraine to investigate Democratic rival Joe Biden and obstruction of Congress in the following investigation.
Trump has branded the case a "hoax" and a "witch hunt" but the White House is girding for a trial that could present damaging evidence against the USA leader on national television over two weeks or more.
Pelosi attacked suggestions by Trump and some of his supporters that the Senate, as soon as the trial opens, vote to dismiss the charges. It would require a rare change in the rules, similar to McConnell's approach to Supreme Court confirmations.
In a letter to her Democratic colleagues, Ms Pelosi said on Friday she was proud of their "courage and patriotism" and warned that senators now have a choice as they consider the charges of abuse and obstruction against the President.
It is about a fair trial. There's nothing that the Senate can do that can ever erase that, she said.
Pelosi said the House vote last month means Trump will be "impeached forever" and "for life".
During his own Sunday morning show appearance, Trump suggested he'd use executive privilege to prevent Bolton from testifying.
One of those retiring senators is Sen.
Democrats want a new testimony, in particular from the former White House security adviser, John Bolton, who has indicated that he will defy Trump's orders and appear when summoned.
Trump has remained committed to blocking any top administration officials, current and former, from testifying. His guilt or innocence would not be officially determined until the Senate votes and with Republicans holding a majority there and the case against the president flimsy at best, it's highly unlikely he will actually get impeached. On Monday, McConnell said Pelosi's "strange gambit has achieved absolutely nothing".
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"No problem other than one thing", Trump said.
"Tomorrow, we will transmit those articles & name impeachment managers".
McConnell has yet to say definitively how the Senate will conduct the trial.
Nadler, D-N.Y., and House Intelligence Committee Chairman Adam Schiff, D-Calif., will most likely lead the team.
McConnell fueled Democratic concerns about dismissing the charges outright when he signed onto a resolution sponsored by Sen. Allies and opponents of President Trump alike can see that impeachment has become a desperate effort to instill fear in the American people ahead of a general election. GOP Senator Rick Scott from Florida said Sunday that he wants to hear about the Bidens "and find out - find out".
It takes just 51 votes to approve rules or call witnesses, meaning four Republican senators would have to side with Democrats to insist on testimony.
It has been nearly four weeks since the House voted to impeach Trump over his dealings with Ukraine.
While some Democrats have grumbled about the delay, Pelosi and other party leaders defended the strategy, saying it produced new potential evidence and turned public attention on the upcoming trial. McConnell is reluctant to call new witnesses who would prolong the process.
"I also have to say that I'm skeptical that Mr. Bolton will appear before the House".
According to the nation's Constitution, the House shall have the sole power of impeachment, while the Senate shall have the sole power to try all impeachments.