Danuta Hübner MEP, a former Polish minister and EU commissioner, said UK would not be able to conclude any trade deal while still a member of the European Union.
Ms Hübner now chairs the European parliament's constitutional affairs committee that will vet any post-Brexit trade deal with the UK.
She stated next year's negotiations over the UK's exit from the EU would be on different tracks from any talks regarding a post-Brexit relationship.
Ms Hübner told The Guardian: "Formally you cannot conclude or even negotiate the agreement that belongs to a third-country situation while you are still a member.
"Article 50 is only about withdrawal and only when you are out can [you] negotiate another agreement."
While she admitted post-Brexit trade deals and Article 50 negotiations would be linked, she said the pair would not be merged.
The Polish MEP said: "Our major challenge is how to ensure that between the withdrawal agreement and the future agreement there is no legal vacuum."
Mr Fox has called on all those involved in the UK's exit from Europe to avoid "a position of ultra-legality" which could cause an unwanted delay in producing a post-Brexit UK-EU trade agreement.
He said: "It makes sense for all parties to take down the political temperature, to stop adopting a position of ultra-legality and get to where we might be able to improve the prosperity of citizens who elect us.
"If we work together, we will not end up introducing, intentionally or otherwise, trade impediments that do not exist at the present time, which can only harm the prosperity of our own people."
The recently signed EU free trade deal with Canada was nearly foiled after Belgium said it could not ratify the treaty due to opposition from the Wallonia regional parliament.
Similarly, Liam Fox was criticised by MPs for not putting the deal to a Commons vote.
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