Senate Minority Leader Chuck Schumer, D-N.Y., on Sunday sent Senate Majority Leader Mitch McConnell, R-Ky., a letter outlining the parameters for a weekslong Senate impeachment trial, including the proposal that former National Security Adviser John Bolton and acting Chief of Staff Mick Mulvaney be subpoenaed to testify.

Bolton and Mulvaney were among four new witnesses whose testimonies Democrats were seeking for the impeachment trial over President Trump's actions toward Ukraine.

In the letter, Schumer proposed the structure for a "fair and honest'' trial, in an attempt to launch negotiations ahead of House voting this week.

Trump is accused of abusing his presidential power by asking Ukraine to investigate his political rival, former Vice President Joe Biden, while holding American military aid as leverage, and obstructing Congress by blocking the House's efforts to investigate his actions. Trump and the White House repeatedly have denied he did anything wrong.

An impeachment vote is widely expected in the Democrat-controlled House, but likely will be quashed in the Senate, where Republicans have held the majority. McConnell has signaled his preference for a speedy trial.

Schumer wrote in his letter that the trial must "be one that not only hears all of the evidence and adjudicates the case fairly; it must also pass the fairness test with the American people."

Schumer also proposed a detailed structure and timeline for a trial to begin Jan. 7, with the swearing-in of Chief Justice John Roberts to oversee the proceedings and stretching for several weeks as Democrats subpoena witnesses and testimony.

A recent book claimed that Bolton labeled the alternative foreign policy being run by Trump attorney Rudy Giuliani and others as a "drug deal," and he wanted no part of it. He left his post in September.

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In addition to Bolton and Mulvaney, Schumer said Democrats also wanted testimony from two other White House officials: Robert Blair, a top Mulvaney aide, and Michael Duffey, a budget official who was tasked with handling the Ukraine issue.

Schumer additionally set out a specific schedule that would allow for 24 hours of opening arguments by the House Democrats' impeachment managers and then 24 hours for the White House lawyers to present their arguments, followed by days of witness testimony.

A spokesman for McConnell told Fox News that the Senate majority leader “has made it clear he plans to meet with Leader Schumer to discuss the contours of a trial soon. That timeline has not changed.”

McConnell has made clear in recent days his preference for a speedy trial without calling witnesses, as other Republicans said they feared it could become a spectacle.

Appearing on CBS News' “Face the Nation'' Sunday, top ally Sen. Lindsey Graham, R-S.C., said he also preferred a swift trial.

"I'd tell the president, if somebody is ready to acquit you, I'd sort of get out of the way," Graham said. He warned that calling witnesses could mean that Trump administration officials such as Secretary of State Mike Pompeo, whom the White House previously blocked from appearing before investigators, could be forced to testify.

"I understand the president's frustration, but I think what's best for the country is to get this thing over with," Graham said. "I clearly made up my mind. I'm not trying to hide the fact that I have disdain for the accusations in the process, so I don't need any witnesses."

Trump has lashed out repeatedly against impeachment and has told confidants that even if he's acquitted in the Senate as expected, it will mark a stain on his legacy.

"The Impeachment Hoax is just a continuation of the Witch Hunt which has been going on for 3 years. We will win!" Trump tweeted Sunday.

Sen. Ted Cruz, R-Texas, said Sunday on ABC News' “This Week” that Trump should be able to call witnesses, including Biden's son Hunter and the whistleblower who reported Trump's July telephone conversation with Ukraine's president.

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Hunter Biden was on the board of a Ukrainian energy company while his father was vice president, and Trump has alleged that Joe Biden got a Ukrainian prosecutor fired because the prosecutor was looking into the energy company. The U.S. and many other Western governments had pushed for the prosecutor's ouster, saying he was soft on crime.

Fox News' Chad Pergram and The Associated Press contributed to this report.