The Labor Department is considering including construction in its plan to expand apprenticeships—potentially creating a showdown with labor groups that oppose this move.

The Associated Builders and Contractors, a trade association representing the nonunion construction industry, has been lobbying the DOL and the White House to include construction in the agency’s still unreleased industry-led apprenticeship program.

“We are advocating for all industries to be included,” Drew Schneider, legislative director for ABC, said.

The DOL previously said construction and the U.S. military would be excluded from the Industry-Recognized Apprenticeship Program, given their high participation rate in the federal Registered Apprenticeship system,...