"The argument for an argument to dismiss is: there was one in the Clinton rules," Blunt said, referring to the impeachment of President Bill Clinton. "But I think I'm safe in saying there's almost no interest in motion to dismiss, certainly there aren't 51 votes for a motion to dismiss."
Over the weekend, Trump argued that a trial would give Democrats a "credibility that it otherwise does not have" and urged Republicans to dismiss the charges against him.
"Many believe that by the Senate giving credence to a trial based on the no evidence, no crime, read the transcripts, 'no pressure' Impeachment Hoax, rather than an outright dismissal, it gives the partisan Democrat Witch Hunt credibility that it otherwise does not have," Trump tweeted. "I agree!"
But Republicans, including Senate Majority Leader Mitch McConnell, have said that dismissing the articles of impeachment against Trump is not a likely scenario. Instead, they have endorsed a vote of acquittal, believing it sends a stronger message.
Several Republican senators are now debating whether or not a "motion to dismiss" should even be included in the rules resolution McConnell is currently drafting, which will determine the procedure senators will abide by during Trump's impeachment trial. During Clinton's trial, the rules resolution included a motion to dismiss, but it ultimately failed.
"Our members, generally, are not interested in a motion to dismiss. They think both sides need to be heard. They believe the president needs to be heard, for the first time, in a fair setting," Blunt said.
Other Republican senators concur.
Sen. Susan Collins of Maine told reporters on Monday, "I would vote against a motion to dismiss immediately. Absolutely."
Utah Sen. Mitt Romney said, "I will not be supporting a motion to dismiss."
Other senators, while they're not commenting on how they'd vote on a motion to dismiss, have said multiple times now that they want a fair trial that allows for the House impeachment managers and Trump's legal team to make their case before the Senate chamber and the American people.
According to several senators, McConnell is finalizing the rules resolution by early this week, and it's likely he will release the rules resolution once the articles of impeachment have been transmitted to the Senate.
On Friday, House Speaker Nancy Pelosi that the House would vote on a resolution this week to name impeachment managers, a move that would trigger the delivery of impeachment articles to the Senate. She's meeting with her caucus on Tuesday morning to take the temperature of her colleagues before making a final determination on the timing to formally send the articles.
ABC News' John Parkinson contributed to this report.