American and European trade representatives met in Washington last week in an attempt to iron out their differences on trade. But talks hit a stalemate after both sides couldn't agree on details that involve the EU buying more U.S. agricultural products, reported CNN.
Last year, Trump threatened to impose tariffs of up to 25 percent on European cars and raised levies on steel and aluminum imports from Europe.
"Trust is really at an all-time low," Marietje Schaake, a member of the European parliament, told CNBC's "Squawk Box."
"The EU is very clear that we want to have rules-based trade, we want to strengthen the multilateral system and we think it is to our mutual benefit to have the U.S. as a partner here," she added. "But President Trump clearly has other ideas. He believes in a more protectionist, nationalist agenda and it's hard to deal with because we don't really know what we can discuss there."
The friction between the U.S. and EU also means that the two sides are missing an opportunity to work together in confronting China's alleged unfair trade practices, said Schaake.
Trump has repeatedly attacked Beijing for practices such as intellectual property theft, barriers to American companies that want to operate in China, and the massive trade imbalance between the two countries.
Such tensions between the world's two largest economies led to a tit-for-tat tariff fight for much of 2018 until Trump and President Xi Jinping agreed in December last year to stop imposing additional tariffs on each other's products as they negotiate a trade deal.
Some of Trump's criticisms of China are shared by the EU, according to Schaake and other European officials.
"I think it is crucial that we talk to the United States, not in the least because we both face challenges from China — a country that is not exactly known for respecting the rules around trade," Schaake said. "So, I think we should actually pursue a shared agenda instead of being divided and opposing each other."
Her view is shared by William Reinsch, senior advisor and Scholl Chair in international business at think tank Center for Strategic and International Studies.
Reinch told CNBC's "Squawk Box" on Wednesday that the U.S. and the EU could together "form what would be the largest middle-class consumer market in the world" with a law-based system that China must adhere to in order to trade with.
"It would be transforming, but (the U.S. and the EU) can't seem to get past all these petty stuff we've been arguing about, really, for 40 years. Whether it's chickens or automobiles or cheese — we can't seem to get past the specifics," he said.