With strains showing up in the relationship between the U.S. President Donald Trump and his Trade Representative Robert Lighthizer, one expert has expressed concerns that Trump would settle for an "inadequate" and "weak" deal with China.

The comment by Niall Ferguson, senior fellow at the Hoover Institution at Stanford University, came after several public disputes between the president and Lighthizer on matters related to the U.S.-China trade war.

Last week, Trump and Lighthizer sparred in front of journalists — and Chinese representatives led by Vice Premier Liu He — over whether "memorandum of understanding" is the right phrase to term the agreement that the U.S. and China are negotiating.

The two sides were reportedly drawing up six MOUs which would form the building blocks of a final deal. But Trump objected to the use of the term, arguing that "they don't mean anything." Lighthizer gave in after some back-and-forth with his boss and opted to use "trade agreement" instead.

"I think the big question ... is whether or not President Trump is going to overrule Robert Lighthizer and take a deal that Lighthizer would regard as inadequate, as weak. I very much hope he doesn't do that because Robert Lighthizer has been doing an excellent job driving a very hard bargain and when Lighthizer says we're not there yet, I take that very seriously," Ferguson told CNBC's "Closing Bell" on Wednesday.

"We saw just the other day the president has the power to overrule [Lighthizer], even in the terminology of the deal ... Robert Lighthizer had to very quickly drop that phrase and get on with the Trumpian language like a 'trade deal,'" he added.