US President Donald Trump OLIVIER DOULIERY | AFP | Getty Images

The European Union (EU) could yet do a tariff deal with the U.S auto sector, despite unhappiness at the hardball negotiating style of President Donald Trump, according to the executive director of the International Trade Centre (ITC). "The EU is saying two things. The first thing… is we will not negotiate under a threat, we will not negotiate with a gun to our head. But the second thing the EU is saying (is) that, alright, if there is a particular sector causing difficulties to the U.S. like vehicles, let’s sit down and discuss," Arancha Gonzalez told CNBC’s Joumanna Bercetche on Wednesday. "It is pretty much in line with what the U.S. talked about a few weeks ago in terms of a ‘zero-for-zero’ tariff deal," she added. The ITC is a subsidiary of the World Trade Organization (WTO) and the United Nations (UN). Gonzalez said the concept of particular sectors being exempt from tariffs was first suggested by Robert Zoellick when he was the U.S. trade representative during the presidency of George W. Bush.

"It is a great idea, but the problem you look at trying to implement it, you will have a number of unhappy sectors. I guess that producers of trucks in the U.S. that currently enjoy the protection of a 20 percent tariff would not be very eager to surrender that protection," she said. Gonzalez's comments come after Trump warned the World Trade Organization (WTO) on Monday that “we’ll be doing something” if the United States isn’t allowed to change the rules on tariff setting. Some have interpreted that as a threat to leave the WTO, but Gonzalez said that was unlikely, given the decision rested with the U.S. Congress, rather than with Trump. “You know there is a mechanism where every year the U.S. has a process to decide whether they want to pull out of the WTO. Since the WTO has been in existence, the answer in Congress has invariably been, ‘No, we want to remain a member of the family.’ I doubt this will change soon,” she said.