Wirtschaftswoche cited "EU sources" as saying a US Department of Commerce investigation report was on Trump's desk, adding: "Trump will possibly decide on tariffs as early as next week after the G20 meeting in Buenos Aires."
The European Commission, which oversees trade policy for the 28-member European Union, declined to comment on the report in general, but did say that Wirtschaftwoche's reference to EU Trade Commissioner Cecilia Malmstrom heading to Washington on Wednesday was not correct.
Neither White House nor the US Commerce Department immediately responded to a request for comment.
The Commerce Department has not publicly released any findings from its investigation into whether imported autos and parts pose a national security risk. Reuters reported that the department submitted its recommendations earlier this month to the White House, which did not immediately act.
Trump could take weeks or month to decide. Once he makes a decision, the White House has 15 days to impose the new tariffs.
European auto stocks extended losses after the report, falling 2.5 percent . Autos stocks are down 20 percent year-to-date as fears of tariffs and slowing growth in car sales drive investors away from the sector.