Democrats are asking to hear from four witnesses -- acting White House chief of staff Mick Mulvaney, former National Security Adviser John Bolton, Associate Director for National Security at the Office of Management and Budget Michael Duffey and senior adviser to the acting White House chief of staff, Robert Blair -- all of whom refused to participate in the House investigation.
Democrats, Schumer says in the letter, are open to additional witnesses with direct knowledge of allegations Trump withheld funding from Ukraine in a bid to get the country to investigate former Vice President Joe Biden and his son, Hunter, who served on the board of Ukrainian gas company Burisma.
"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 wrote in his his letter to McConnell. "That is the great challenge for the Senate in the coming weeks."
As for the timeline, Democrats propose pretrial housekeeping measure be adopted on Jan. 6, followed by the swearing-in of the chief justice and senators on Jan. 7. House managers would make their presentations on Jan. 9, for no more than 24 hours, followed by the president's counsel, for no more than 24 hours.
Of course, the House has yet to formally vote on the articles of impeachment. The Democrat-controlled House is expected to approve the articles.
On Friday, the House Judiciary Committee voted along party lines to approve two articles of impeachment against Trump, sending them to the full House for historic final votes expected Wednesday.
The committee recommended charges of abuse of power and obstruction of Congress to the full House.
"In a short time, the House of Representatives is expected to approve Articles of Impeachment against President Donald J. Trump," Schumer wrote. "In response to the House's action, as you have noted, our rules require the Senate to conduct a trial to consider and vote on the Articles of Impeachment. This is an enormously weighty and solemn responsibility that was assigned to the Senate by the Framers of the Constitution."
McConnell has said he will coordinate with the White House to make plans for the impeachment trial.
"Leader McConnell has made it clear he plans to meet with Leader Schumer to discuss the contours of a trial soon," Doug Andres, McConnell spokesman, told ABC News. "That timeline has not changed."
ABC News' Mariam Khan contributed to this report.