Argentina claims sovereignty over the British-governed islands in the south Atlantic, over which the two nations fought a short but deadly war in 1982.
"It is true that the European Union, through the EU agreements, is bonded very firmly and very strongly to the United Kingdom," Foreign Minister Susana Malcorra said in Brussels when asked whether Brexit would affect the diplomatic situation regarding the Falklands, which Buenos Aires calls Las Malvinas.
"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" in its position, she added.
"But I think it is still very preliminary, Brexit has just started and there are multiple themes. So, we follow closely."
Under the EU's 2009 Lisbon Treaty, the Falkland Islands are a British overseas territory to which some EU rules apply.
The Falklands conflict -- which came after Argentine troops invaded and Britain's then premier Margaret Thatcher sent in a naval task force -- claimed the lives of 649 Argentine troops, 255 British soldiers and three islanders.
But it remains a live issue on both sides, with a former British political leader earlier this month even comparing a dispute with Spain over Gibraltar's post-Brexit fate to the Falklands conflict.
Michael Howard, a former leader of the ruling Conservative Party, said that current leader Theresa May would "show the same resolve" on Gibraltar as Thatcher had on the Falklands.
Spain said it was "surprised" by the comment.
In 2013, almost 100 percent of the Falkland Islands' residents voted in favour of remaining under British rule.
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