At the close, the Dow Jones industrial index had fallen 0.3 percent, the broad S&P 500 index was unchanged and the Nasdaq's technology-heavy composite index rose 0.1 percent.
Earlier, the Financial Times reported, citing three sources, that Trump is demanding tariffs of at least 15-20 percent in an agreement with the EU. The President's deadline of August 1 is approaching, when he threatens to introduce 30-percent tariffs on the majority of imports from the EU.
Trump is also said not to have wavered on the EU's urgings regarding the 25-percent tariffs he has imposed on car imports, according to the FT.
Among today's losers were, among others, the streaming service Netflix, down 5.1 percent, despite having reported quarterly figures on Thursday that exceeded market expectations for profit and sales. Credit card giant American Express also fell 2.4 percent.
Soda and snack company Pepsico, which also reported quarterly figures on Thursday, rose 1.5 percent in turn. Electric car giant Tesla also rose 3.2 percent.