(NewsNation) — Media reports suggest ending the military COVID-19 vaccine mandate, which has been a sticking point for Republicans, could be a part of the annual National Defense Authorization Act.

Rep. Adam Smith, (D-Wash.), who chairs the House Armed Services Committee, said Saturday that rolling back the policy is possible for a compromise version of the National Defense Authorization Act, according to Politico.

“We haven’t resolved it, but it is very fair to say that it’s in discussion,” he told the news outlet.

While Rep. Hakeem Jeffries of New York, the incoming House Democratic leader, said he didn’t want to comment on aspects of the National Defense Authorization Act that aren’t finalized, but added that members of his party would likely support the defense bill.

“Let’s see what the final product is, but I plan to support it,” he said on Tuesday.

House Minority Leader Kevin McCarthy (R-Calif.) claimed he worked out an arrangement to stop the mandate, although White House officials later disputed that characterization, according to the Washington Post.

“Leader McCarthy raised this with the President, and the President told him he would consider it,” spokeswoman Olivia Dalton said in a statement to The Post. “The Secretary of Defense has recommended retaining the mandate, and the President supports his position. Discussions about the NDAA are ongoing.”

Sources, though, aren’t ruling out that a separate bill could also be created to ax the mandate.

“If we can just stop the bleeding and stop the vaccine mandate from damaging our soldiers, our men and women in uniform, then that would be an enormous victory for those who are trying to serve our country,” Rep. Chip Roy, a Texan Republican, said.

The Pentagon began requiring COVID vaccines for all military members last year. Around 3,400 troops were dismissed for not complying about six months later.

Last week, over a dozen Republican senators threatened to delay a vote for the National Defense Authorization Act if the vaccine requirement was not removed. Sen. Rand Paul (R-Ky.) said at a recent press conference that 20 Senate Republicans have signed a letter saying they will vote against cloture on it, NewsNation partner The Hill reported.

Right now, the Biden administration and Defense Secretary Lloyd Austin support enforcement of the mandate, saying it’s an important safeguard to protect the readiness of the U.S. military.

“The Pentagon has a range of vaccines,” press secretary Karine Jean-Pierre said. “It has long (been) required, so this is nothing new….there’s history here. There’s precedent. So with respect to NDAA, those discussions are ongoing. I don’t want to get ahead of it.”

Lawmakers have about two weeks left to pass the National Defense Authorization Act, which guides Department of Defense activities, appropriations and programs for the upcoming fiscal year.

While the bill is expected to remove the mandate it is not set to reinstate those service-members discharged or who had their benefits taken away for refusing to get the vaccine.