"I've talked to anywhere from five to 10 of my colleagues who have very severe misgivings about the direction that Mitch McConnell is going in denying a full, fair proceeding with witnesses and documents," Xinhua news agency reported citing Richard Blumenthal, a Democrat from Connecticut, as saying in a news briefing.
Trump was impeached on December 18 by the Democratic-controlled House of Representatives over abuse of power in his dealings with Ukraine and obstruction of Congress.
The Republican-majority Senate is expected in January to hold the impeachment trial to decide whether to convict the president and remove him from office.
While the Democrats have urged the Republicans to call witnesses including current and former senior White House officials and demanded relevant documents, McConnell - although not ruling out calling witnesses - has indicated a quick process to acquit Trump.
"Everything I do during this, I'm coordinating with White House counsel," McConnell had said in a TV interview earlier this month before the impeachment.
"There'll be no difference between the president's position and our position as to how to handle this."
Commenting on those remarks, Lisa Murkowski, Republican senator representing Alaska, said that she was "disturbed".
"To me it means that we have to take that step back from being hand in glove with the defense, and so when I heard what Leader McConnell has said, I happened to think that further confused the process," Murkowski said.
Blumenthal said his hope is that Republicans "will say publicly what Senator Murkowski did, and really hold Mitch McConnell accountable".
The House is yet to send the articles of impeachment to the Senate.
House Speaker Nancy Pelosi, a California Democrat, has said that she was waiting for the rules governing the trial to be set, expressing fairness concerns.
( With inputs from IANS )