(Reuters) - National Mediation Board, a U.S. federal labor-management relations agency, is considering a proposal to allow airline workers to form unions with the majority approval of those voting, Bloomberg news agency said, citing people familiar with the matter.

AFL-CIO, the largest U.S. labor federation had asked the board for a rule change that would base the outcome of union elections at airlines on the number of votes cast instead of on the majority of eligible members of a worker group.

Delta Air Lines Inc, which bought Northwest Airlines in October 2008 to form the world's biggest carrier, has opposed the AFL-CIO's request for a rule change.

"It's been our sincere hope that the National Mediation Board would look at our recommendations favorably," Edward Wytkind, head of the AFL-CIO's transportation trades department, told Bloomberg.

The National Mediation Board could not be immediately reached for a comment by Reuters outside of U.S. business hours.

(Reporting by Sakthi Prasad in Bangalore; Editing by Valerie Lee)