(CNN) Sen. Cory Gardner, the chairman of the National Republican Senatorial Committee, said Monday that if Alabama Republican Senate nominee Roy Moore "refuses to withdraw and wins, the Senate should vote to expel him."
Gardner said in a statement, "he does not meet the ethical and moral requirements of the United States Senate."
There have only been 15 expulsions in US Senate history.
Earlier Monday, Senate Majority Leader Mitch McConnell told reporters that Moore should step aside. Later McConnell was asked as he left the US Senate floor, if Moore should be expelled if he is elected.
"I said this morning all I'm going to say today," McConnell responded. "And others are speaking for themselves and you all are reporting it."
McConnell would not answer a question about whether he thinks there would be enough GOP votes to expel Moore if it came to it.
Gardner's comments come as two senior GOP sources said that top Senate Republicans are skeptical of the idea that incumbent Republican Sen. Luther Strange will run as a write-in candidate, because they don't think he can win.
Despite the calls from some GOP senators for Strange, who was appointed to the position and lost a GOP primary to Moore, to run, discussions between the leadership and Strange have focused on whether he can win a last-ditch campaign. And there has been a consensus among some top Republicans that Strange has little chance to win as a write-in, these sources say.
Sen. Lisa Murkowski, an Alaska Republican who won a write-in Senate race, said she talked to Strange about running as a write-in candidate. Utah Republican Orrin Hatch said Monday "I believe Luther Strange is an excellent alternative."
Last week, The Washington Post published a report based on interviews with more than 30 people, saying Moore pursued relationships with teenage women while he was in his 30s. One woman said she was 14 years old when Moore initiated sexual contact with her. On Monday, a separate Alabama woman alleged Moore sexually assaulted her when she was a minor, her attorney Gloria Allred said.
McConnell on Moore: 'I believe the women,' Moore should go
Moore denied wrongdoing following the Post report last week and said he planned to sue them this weekend. The Moore campaign released a statement Monday following the newest accuser denying Moore had "any sexual misconduct with anyone."
"Gloria Allred is a sensationalist leading a witch hunt, and she is only around to create a spectacle," Moore campaign chairman Bill Armistead said in a statement. "Allred was the attorney who claims credit for giving us Roe v. Wade which has resulted in the murder of tens of millions of unborn babies. We've said this before and we'll say it again: Judge Moore is an innocent man and has never had any sexual misconduct with anyone. This is a witch hunt against a man who has had an impeccable career for over 30 years and has always been known as a man of high character."