Julia Hartley-Brewer had a passionate dispute with an editor over terms of leaving the EU.
Negotiations to decide the future relationship between Britain and the EU are due to begin next week.
Ahead of them, negotiatior-in-chief Guy Verhofstadt has said that Britain might be able to remain in the union, but without the perks of being a member.
Dan Roberts, the Brexit editor at The Guardian, said this should be taken with "a pinch of salt" in an interview with Julia Hartley-Brewer.
He said: "We’re all long way from this at the moment.
"We need to remember Brussels is not homogenous. Guy is a liberal MEP in the European Parliament.
"The president is a key figure there and he was upbeat about keeping the door open."
When the discussion turned onto Theresa May's strategy of a good deal or no deal in what's seen as a hard Brexit, Julia and her interviewee clashed over the terms of what a vote for Brexit meant.