The EU's top trade official said today it was unrealistic to hope that the Trump administration could permanently exempt the EU from steel and aluminium tariffs before they kick in on June 1.
EU countries have tried to woo the US away from punishing steel and aluminium tariffs and win Europe a similar break as handed to China.
Europe was hit by the shock tariffs in March, part of the protectionist US president's threat of an "America First" trade war with Washington's closest partners, including Canada, Mexico and Japan.
Trade Commissioner Cecilia Malmstrom told European Parliament deputies that even if the US refrained at the last minute from applying duties, "I expect them nonetheless to want to impose some sort of caps on EU exports".
A "hard cap" allowing no further exports beyond a quota would be worse for the EU than a "soft cap", under which exports would still be possible beyond the limit but subject to duties, she said.
Malmstrom said ideally there would be no tariffs or quotas at all "but realistically I don't think we can hope for that".
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The European Union has said it refuses all trade talks with the United States unless Washington grants a permanent exemption from the painful tariffs.
Europe has threatened to retaliate with European tariffs on American imports, including iconic items such as Harley-Davidson motorbikes and bourbon whiskey.
These counter-measures will officially become enforceable on June 20, but Europeans have committed to not use them as long as talks with the US are ongoing.
Malmstrom is to meet with US Commerce Secretary Wilbur Ross in Paris on Wednesday on the margins of a meeting of the Organization for Economic Cooperation and Development in Paris, the European Commission said.