BERLIN—The Trump administration is considering inviting the CEOs of Germany’s three largest car makers to the White House amid growing impatience in Washington at the slow pace of talks with the European Union on forging a trans-Atlantic trade deal, according to people familiar with the discussions.

The chief executives of Volkswagen AG, BMW AG and Daimler AG could meet with Chief White House economic adviser Lawrence Kudlow, Commerce Secretary Wilbur Ross, and Trade Representative Robert Lighthizer within days, according...