(CNN) Senate Majority Leader Mitch McConnell is expected to hold a final vote to acquit President Donald Trump, should he be impeached, when a majority of senators believe his trial has run its course instead of holding a vote on dismissing the articles of impeachment, two Republican senators told CNN on Wednesday.

Republicans want to have a vote on acquittal -- to clear the President of the charges against him -- not simply rely on a 51-vote threshold procedural motion to dismiss the hotly disputed case.

The Constitution mandates 67 votes are required to convict the President and remove him from office, a barrier widely considered too high to be reached in this case.

One vote McConnell can't rely on is that of Vice President Mike Pence, who has "no role in impeachment," according to a GOP leadership aide, despite being president of the Senate with the mandate to break ties.

Pence's power, which applies to legislation and nominations, isn't in effect when the Senate is weighing removing his boss, an obvious conflict of interest since he would replace Trump if he were removed. Instead, Supreme Court Chief Justice John Roberts would preside at the trial and any tie motions would fail.

One of the senators, speaking anonymously, said McConnell would not call a vote on a motion to proceed to the impeachment articles unless he knew he had the 51 votes needed to end the trial, which would then set up a final vote on the articles themselves. On that final vote, 67 votes would be needed to convict Trump and remove him from office.

The other senator, Sen. John Cornyn of Texas, said it "would make more sense" to move to vote on the articles of impeachment -- with their 67-vote requirement -- than on a motion to dismiss and "decide this on a 51-vote threshold, with the potential tie and all the recriminations that would flow from that."

McConnell hinted at this strategy when he spoke to reporters on Tuesday and said the Senate would have two choices after hearing opening arguments from the House impeachment managers and the President's defense counsel.

"It could go down the path of calling witnesses and basically having another trial or it could decide -- and again, 51 members could make that decision -- that they've heard enough and believe they know what would happen and could move to vote on the two articles of impeachment," he said. "Those are the options. No decisions have been made yet."