In a weekend post on the social media site Twitter, Trump threatened to hit car exports from the European Union, should Brussels make punitive changes to its trade duties.
The tit-for-tat exchange originated after Trump had earlier announced a 25 percent tariff on steel and aluminum.
Speaking to CNBC Monday at the Geneva International Motor Show, VW Group chief Matthias Mueller said there was no need to make any pressing decisions.
"We haven't assessed that yet because apart from a rumor that things are reputed to change, the regulations have not changed," he said.
"We are calmly assessing the situation and will take the necessary decisions," Mueller added.
One expert told CNBC that any war of words between Trump and the EU could lead to some serious pressure on the German auto industry.
Also speaking Monday was Audi Chairman Rupert Stadler who told CNBC he preferred to see "open and free trade" across the auto industry.
When pressed on whether he would move production capacity into the U.S. to avoid tariffs imposed by Trump, Stadler said such a move would have to fit with his firm's long-term strategy.
"I think in the premium sector it is a little bit easier because it is not so price sensitive, but nevertheless we have to watch and listen," Stadler said.
VW Group's operating profit in 2017 nearly doubled to a record 13.8 billion euros ($17 billion) from $7.1 billion the previous year. However, the firm has anticipated sales in 2018 to be checked by huge investment into electric and self-driving cars.
VW is also still paying out for the "Dieselgate" scandal which is estimated to have cost the German firm around $25 billion in the U.S. alone. Mueller said Monday that the scandal was now in the past, but argued that the internal combustion engine would shortly "see a renaissance" and diesel would have a part to play.
At the Geneva International Motor Show, Volkswagen Group will launch its I.D Vizzion concept, thought to be a fully autonomous luxury people-mover.
Aside from the VW brand, the firm will also display new offerings from its Audi, Skoda, SEAT, and Porsche brands.