The policy language under discussion would end the ban from the national organization's rules, leaving local sponsoring organizations the ability to decide for themselves whether to admit gay scouts, NBC News reported Monday.
"The chartered organizations that oversee and deliver scouting would accept membership and select leaders consistent with their organization's mission, principles or religious beliefs," said Deron Smith, a spokesman for the Boy Scouts' national organization.
Individual sponsors and parents "would be able to choose a local unit which best meets the needs of their families," Smith told NBC News.
Sources outside of BSA said discussions on the potential policy change are nearly finished. If approved, the change could be announced as soon as next week after the organization's national board has its regular meeting.
Last summer, the Boy Scouts, based in Irving, Texas, affirmed a policy of banning gay members after a committee's nearly two-year examination of the issue.
Since then local chapters have been urging national leaders to reconsider.
Also, more than four dozen local United Way groups, along with several corporations and charities, determined the ban violates their non-discrimination requirements and stopped providing financial aid to the Boy Scouts, NBC News said.
The national scouting organization sets broad policies but the more than 290 local councils oversee day-to-day conduct of the more than 116,000 local organizations. Individual troops are sponsored by religious and civic organizations.
The policy change under discussion "would allow the religious, civic or educational organizations that oversee and deliver scouting to determine how to address this issue," Smith said.
In 2000, the U.S. Supreme Court ruled the Boy Scouts were protected by the First Amendment right of free expression for the organization's belief that homosexual conduct is inconsistent with values stated in the Scout oath.