Outgoing GOP Sen. Luther Strange is being urged to mount a write-in campaign in Alabama’s Senate special election next month amid the fallout over a bombshell report that Republican nominee Roy Moore pursued romantic relationships with teenagers as an adult.

Among those encouraging Strange to consider a write-in campaign is Alaska Sen. Lisa Murkowski, who famously won as a write-in candidate in 2010 after being defeated in the Republican primary. A spokeswoman for Murkowski told Fox News the Alaska senator thinks Moore should step aside if the allegations are true and Strange should seek the seat as a write-in.

Strange, who was appointed to Alabama’s Senate seat when then-Sen. Jeff Sessions vacated it to become attorney general, was defeated by Moore in a bruising run-off in September. He was seen talking with Senate Majority Mitch McConnell on the Senate floor after the story broke Thursday afternoon.

Speaking to reporters on Capitol Hill on Thursday, McConnell, R-Ky., did not respond to questions about whether he would support Strange as a write-in candidate.

TRUMP: MOORE WILL 'STEP ASIDE' IF ALLEGATIONS ARE TRUE

The Washington Post reported that Moore, the former chief justice of Alabama’s Supreme Court and an ardent social conservative, pursued relationships with four teenage women dating back to the 1970s when he was in his early thirties and single. One woman told the paper she was 14 when the 32-year-old Moore asked her out and made sexual advances.

Moore, 70, says the accusations are false and calls the story a “desperate political attack.”

Moore also lashed out via Twitter at what he called "the Obama-Clinton machine's liberal media lapdogs," saying: "The forces of evil will lie, cheat, steal –– even inflict physical harm –– if they believe it will silence and shut up Christian conservatives."

An error occurred while retrieving the Tweet. It might have been deleted.

Top Senate Republicans including McConnell, who backed Strange during the primary, have said Moore should step aside if the allegations are true.

A spokesman for Strange did not return a request for comment about the possibility of a write-in campaign.

Under Alabama’s “sore loser” law, Strange’s name could not appear on the general election ballot. But he could run as a write-in.

According to Alabama’s secretary of state’s office, “there are no existing stipulations that prohibit” a write-in candidate “from being elected despite having unsuccessfully run for a party’s nomination, which would normally apply due to Alabama’s sore loser law.”

In Alabama, Republicans expressed skepticism Thursday that Strange could defeat Moore and Democratic nominee Doug Jones as a write-in candidate.

“If he ran a write-in, it would elect Doug Jones for sure,” an Alabama operative with ties to the state’s congressional delegation told Fox News.

Another Alabama political operative doubted the Washington Post report would take down Moore, noting how the socially conservative state still overwhelmingly voted for Donald Trump in the 2016 presidential race after the “Access Hollywood” video surfaced of him using vulgar and sexual language in the past.

Roy Moore is denying the allegations in The Washington Post. (AP)

A well-known elected GOP officeholder in Alabama also poured cold water on the write-in speculation. “I think it would be a huge mistake for Luther to mount a write-in campaign. He lost the nomination for a reason and that hasn’t changed. Write-in campaigns succeed only under the best of circumstances and Luther is far too damaged to meet that test,” the source said.

The Senate Leadership Fund, which poured millions into this summer’s primary in Alabama on behalf of Strange, has not commented on the prospect of Strange as a write-in candidate. But they have called for Moore’s removal.

"If there’s even a shred of evidence to these accusations, Gov. Ivey and the Alabama Republican Party need to do everything in their power to remove Judge Moore from the ballot,” Senate Leadership Fund President and CEO Steven Law said. “There is no place in our party for sexual predators."

In a statement Thursday evening, Alabama Republican Gov. Kay Ivey said she needed to learn more about the accusations before commenting further.

“These allegations are deeply disturbing,” she said. “I will hold judgment until we know the facts. The people of Alabama deserve to know the truth and will make their own decisions.”

Fox News’ Jason Donner contributed to this report.