In a statement, Romney did not raise any objections to holding a vote on a Trump nominee this year and said, "If the nominee reaches the Senate floor, I intend to vote based upon their qualifications."
With momentum from their conference behind a quick vote, GOP leaders are now making clear they are pressing ahead to get the nomination confirmed before Election Day, which would amount to one of the quickest proceedings in modern times. And it comes despite Senate Republicans' refusal to move on then-President Barack Obama's nomination of Merrick Garland to a seat in 2016 when they said his choice -- eight months before November -- was too close to the elections.
Senate Majority Whip John Thune told CNN on Tuesday, "I think it would be a good idea to move forward." He said the timing is not nailed down yet and Republican senators will discuss it at lunch Tuesday.
Senate Majority Leader Mitch McConnell gave a full-throated defense of his decision to move forward quickly with a Supreme Court confirmation process so close to an election.
"Moving ahead with a vote on the forthcoming Supreme Court nomination will be consistent with both history and precedent," McConnell said in remarks on the floor.
McConnell and other Republicans have been fending off accusations from Democrats of hypocrisy over moving forward with a new nomination now after blocking Obama's nominee to the high court following the death of Justice Antonin Scalia in February 2016.
The high-stakes election year battle over the addition of a new justice to the Supreme Court stands to have profound consequences, both for the court by pushing it in a more conservative direction for decades to come and for the ongoing fight for control of Congress and the White House.
Senate Republicans are now laying the groundwork for a quick confirmation process and vote, including planning October confirmation hearings.
Senate Judiciary Chairman Sen. Lindsey Graham said Tuesday that the committee plans to hold three days of hearings for the SCOTUS nominee in October.
"Yeah, trying to keep the process like we had before," said Graham, a South Carolina Republican, when asked if the committee will hold three days of hearings.
Thune said that he expects that once the Senate finishes the government funding bill either this week or next most senators will leave town for much of October as was planned before the passing of the late Justice Ruth Bader Ginsburg. Senators up for reelection are anxious to get home to campaign.
Meanwhile, members of the Judiciary Committee will work to prepare for hearings, meeting with the nominee, and eventually convening hearings.
A new justice on the Supreme Court before November 3 could have major implications for future high court decisions over health care or any election year disputes.
Graham, who is up for reelection, touted Barrett, telling reporters, "I think she'd be a great choice."
Romney said Barrett when asked his view, "I haven't reviewed her judicial record to this point. And will look forward to doing so if she's the nominee."
Asked by CNN if Barrett is chosen whether that would bring the issue of abortion front and center in the election, Graham downplayed the possibility, and replied: "I think every issue is gonna be thrown at the nominee."
Currently, there are 53 GOP senators -- meaning Republicans can only lose three votes to advance the nomination if Vice President Mike Pence stepped in to cast a tie-breaking vote.
Collins on Tuesday specified that she would vote against anyone Trump names if a vote is held prior to the election.
"I made it very clear, yes, that I did not think there should be a vote prior to the election," Collins said, adding, "and if there is one, I would oppose the nominee, not because I might not support that nominee under normal circumstances, but we're simply too close to the election."
It is unclear if there will be any further defections within GOP ranks.
Adding further momentum to an election-year Supreme Court confirmation, Republican Sen. Shelley Moore Capito of West Virginia also came out on Tuesday in favor of moving forward with the process.
"President Trump and the Republican Senate, both elected by the American people, should act to fill the Supreme Court vacancy left by Justice Ginsburg's passing," the West Virginia Republican wrote in a statement on Tuesday.
Romney on Tuesday declined to discuss a hypothetical of a lame duck session vote on the vacant seat if Trump loses the election.
"I'm not going to look at all the hypotheticals that might occur," he said. "But I've laid out what I intend to do and that would be... not dependent upon the timing."
Pressed further, Romney replied, "I've indicated what I intend to do is to proceed with the consideration process and if a nominee actually reaches the floor, that I will vote and based upon the qualifications of that nominee."
This story has been updated with additional developments Tuesday.
CNN's Ted Barrett and Ali Zaslav contributed to this report.