In his letter sent to McConnell on Sunday, Schumer called for at least four witnesses to testify former National Security Adviser John Bolton; Acting White House Chief of Staff Mick Mulvaney; Robert Blair, Mulvaney's senior adviser; and Michael Duffey, Associate Director for National Security at the Office of Management and Budget, reports Xinhua news agency.
"Senate Democrats believe strongly, and I trust Senate Republicans agree, that this trial must be one that is fair, that considers all of the relevant facts, and that exercises the Senate's 'sole power of impeachment' under the Constitution with integrity and dignity," Schumer wrote.
"I also propose that the Senate issue subpoenas for a limited set of documents that we believe will shed additional light on the administration's decision-making regarding the delay in security assistance funding to Ukraine and its requests for certain investigations to be announced by the government of Ukraine.
"This will be a narrowly drawn request limited to electronic communications, memoranda and related records of the relevant senior officials in the White House, Office of Management and Budget, and Department of State," he added.
McConnell said on December 12 that he would be "in total coordination" with the White House in determining the Republican strategy for the looming impeachment trial against Trump.
"Everything I do during this I'm coordinating with the White House Counsel. There will be no difference between the President's position and our position as to how to handle this," McConnell said.
"There's no chance the President will be removed from office."
On December 13, the Democrat-led House Judiciary Committee passed two articles of impeachment, accusing Trump of abusing power and obstruction of Congress.
Trump will be impeached if the House approves either of the two articles by a simple majority vote.
Under the US constitution, the House has the sole power of impeachment while the Senate can try all impeachments.
Conviction can only happen in the Senate and requires at least two-thirds of its members, or 67 senators, to vote in favour after a trial.
Currently, the Senate has 53 Republicans, 45 Democrats and two Independents.
( With inputs from IANS )