Mr Faurie, Argentina’s foreign minister since June 2017, made the shocking claim during an interview with The Telegraph.
Referring to ‘Las Malvinas’, the Argentinian name for the Falklands Islands, he said: “Our planning for Las Malvinas is to have a negotiation that will enable stronger relations between the people on the islands and the people on the mainland.
“We hope that the no-deal Brexit solution will enhance the possibility of that dialogue to be truly one with results.”
Argentina has claimed ownership of the Falklands Islands since 1833.
In 1982, a previous Argentinian government seized the Falklands Islands by force, sparking a short and unsuccessful war with the UK.
Mr Faurie argued EU countries will reduce or end their support for the British claim of the islands after Brexit.
In this situation, he said: “Member states of the EU would not sustain the Malvinas claim in favour of the UK.
“We are there to negotiate, to see what would be the best solution for the people in the islands to be much more in touch with Argentina.”
EU members are obliged, via the ‘Duty of Sincere Cooperation’ principle, to support each other in territorial disputes with non-members. This will end when the UK leaves the bloc.
The EU’s 2009 Lisbon Treaty specifically designated the Falklands Islands as a British overseas territory.
Theresa May will meet Mauricio Macri, President of Argentina, during a G20 meeting in Buenos Aires later this month.
She will be the first British Prime Minister to visit the country since 2001.
The talks are theoretically focused on post-Brexit trade opportunities, but the status of the Falklands Islands could well be raised.
Susana Malcorra, Mr Faurie’s predecessor as foreign minister, was clear that Argentina sees Brexit as an opportunity to undermine European support for the UK.
Last year she said: “It is true that the European Union, through the EU agreements, is bonded very firmly and very strongly to the United Kingdom.
“So when Brexit takes place, the EU could evaluate a decision on how to proceed and how to stand on these issues and there may be a change.”