Union President Ron Gettelfinger confirmed the meeting after a charity appearance in Washington, D.C., on Thursday night but would not elaborate.
A local union official said no agreement has been reached but the meeting was called to discuss labor talks. The official asked not to be identified because the talks are confidential.
Ford and the union have been in talks since August about contract concessions that would match those granted to Chrysler Group LLC and General Motors Co. before they entered bankruptcy protection.
Ford is the only Detroit automaker to avoid bankruptcy court.