The White House hopes language on a possible health-care deal can come as early as Friday or Saturday, leaving the potential for an agreement next week, a White House official told CNBC.

It would be legislative text added as an amendment to the American Health Care Act, the bill that could not clear the House last month, NBC News reported. The Senate Budget Committee is giving technical assistance with the language.

Republicans have struggled to reach a compromise agreement to replace the Affordable Care Act that balances the concerns of both the conservative and moderate wings of the party. An attempt to replace President Barack Obama's landmark health-care law failed last month as House Republicans could not gather enough support.

President Donald Trump has pushed for a vote next week, which may prove daunting as Congress returns from a recess with only days before the current resolution funding the government runs out on April 28.

It is unclear if the revised version of the health-care plan reported by multiple outlets Thursday could gather the votes needed to pass the House.

The Senate Budget Committee is involved to make sure the plan complies with the Byrd Rule, which governs whether Congress can use the budget reconciliation process to lower the vote threshold.

A Senate GOP aide said Friday that budget committee staffers are lending their expertise to make sure the bill language complies with the reconciliation process in the Senate.

They are checking to see if the bill has too many extraneous provisions to be considered a reconciliation bill, which governs whether the Senate can lower the vote threshold to a simple majority in the 100-member Senate, not 60 votes.

The aide offered no timeline for that work to be completed.

Watch: Senate Budget Committee working on health care language