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....