The Hall of Fame basketball player, who considered running for governor of the state in 2014, said if he still lived in Alabama, he would vote for Democratic Senate candidate Doug Jones.
If Moore wins the December 12 special election, for the old seat of Attorney General Jeff Sessions, Senate Majority Leader Mitch McConnell, R-Ky., has said that the Ethics Committee will investigate the allegations and the Alabamian could face an expulsion vote.
"I want to be on the side of right when history writes the story", he said of distancing himself from Moore.
President Donald Trump suggested Sunday that he'd rather see an alleged child sex abuser in Congress than a Democratic "puppet" who will not support the Second Amendment and border enforcement.More news: Doctor Who star Tom Baker returns as Time Lord
Trump's attack Sunday echoed comments he made last week when he called Jones "soft on crime".
Just Tuesday, longtime Michigan Rep. John Conyers acknowledged that his office settled a sexual harassment complaint involving a former staffer, though he "vehemently" denied allegations in the complaint. "Majority are Trump voters", Trump said.
Moore has repeatedly denied the allegations. Faye served as a Gadsen police officer for 37 years and says she worked as a juvenile detective, explaining that every day her department "waited for a complaint to come in" about Roy Moore.
Jones told reporters Sunday that his record speaks for itself and said health care, the economy and education are the top concerns in Alabama.More news: Hornets C Howard fined for obscene gesture
"The moral of the story is: Don't nominate somebody like Roy Moore who could actually lose a seat that any other Republican could win", Graham said. "And you know, you have to listen to him also".
In an interview with John Catsimatidis on AM 970 in New York, Ms McDaniel said the claims against Mr Moore are concerning - but that Alabama officials have maintained he can not be replaced on the ballot. Moore, however, has insisted that he is innocent of the charges. Earlier this month, Moore was accused of sexually abusing girls as young as 14.
But Graham said when it comes to Moore, it's unclear "what winning looks like".
Is it simpler to believe that, while the victims of Louis C.K., Al Franken and Charlie Rose's unwanted advances are telling the truth, Moore's accusers are all liars, operatives in a bipartisan plot by two parties who can't even work together on health care or tax reform?More news: Winnipeg police launch video to help stop gender-based violence
Moore wasn't the President's first choice for the nomination.