If the report is true, then that's good news for auto makers and that should provide some relief for European stocks on the day - since the United States is likely to call back their proposed tariffs on EU cars.
After months of back-and-forth, retaliatory tariffs between the USA and the European bloc, Trump wants to see all tariffs removed on all industries, including agriculture, steel aluminum and medical equipment, according to the official.
The bloc is expected to seek a limited free-trade agreement on industrial goods and for such an agreement to be possible, cars would need to be included, the person said.
"The European Union is nearly as bad as China, just smaller", Bloomberg also quoted Trump as saying.
In a press release the White home says that imported from Brazil, South Korea and Argentina metal and aluminum won't be topic to duties. SUVs assembled by the German carmakers in the American South dominate the models exported to Europe from the US.
Vehicle makers and suppliers are the third-worst performing sector this year on the wider Stoxx Europe 600 index of the region's most valuable companies.
However, speaking to Bloomberg, Trump described the European Union as "almost as bad as China, just smaller".
European Commission President Jean-Claude Juncker told the German ZDF network on Friday that "the people want that, and we will make it happen".
Malmstrom also insisted that whatever deal was reached would fall well short of the ambitions of the TTIP talks, an earlier attempt by Brussels and Washington to reach a wide-ranging trade deal that collapsed after the protectionist Trump took office.
"The people want it, so we will do it".
Errol Taylor, chief executive of the Royal Society for the Prevention of Accidents, said: 'We cautiously welcome the findings. "Our country is stronger than it's ever been financially". The president told aides he supports tariffs on an additional $200 billion in Chinese goods as early as next week, according to Bloomberg.