"I think we might have a couple," of Democratic senators who will join the Republicans not to convict Trump in the trial, Xinhua news agency reported citing Georgia Senator David Perdue as saying to The Hill website on Thursday.
"I don't want to speculate on who, obviously that puts too much pressure on them, but I really think we have people on both sides that are trying to get to a reasonable, non-partisan answer," he added.
Trump was impeached on December 18 by the Democratic-controlled House of Representatives over his abuse of power in his dealings with Ukraine and obstruction of Congress.
At the time of the full House vote, two Democrats voted against the first article of impeachment alleging that Trump abused his power, and three voted against the second purporting that the president obstructed Congress.
Tulsi Gabbard, the Hindu Democrat from Hawaii, voted "present" for each.
In an interview with Fox News on December 12, Senate Majority Leader Mitch McConnell said "it wouldn't surprise" him if "one or two Democrats" in the Senate vote against convicting Trump.
"It looks to me over in the House, the Republicans seem to be solid and the Democrats seem to be divided," the Kentucky Republican added.
Responding to a request for comment on McConnell's remarks, Doug Jones, a Democratic Senator from Alabama, told ABC News on Sunday that he had "no idea what Mitch McConnell's talking about these days".
While stressing the seriousness of the allegations against Trump, Jones said there are "gaps" to be filled.
Trump is impeachable if what he has been accused of are proven true, "but if those dots aren't connected and there are other explanations that I think are consistent with innocence, I will go that way too", he added.
According to news reports, Trump's Senate trial could begin next month, after the holiday break.
However, Trump, the third President in US history to be impeached, was unlikely to be removed from office because of the Republican control of the Senate.
Republicans currently hold 53 seats in the 100-seat chamber, making a conviction - which requires a two-thirds vote - extremely unlikely.
( With inputs from IANS )