Britain could reportedly lose its leading position within the North Atlantic Treaty Organisation (Nato) due to the changed dynamic after Brexit.
The tradition that a British officer holds the number two military post in the alliance after the US is under threat as other European countries eye the coveted role, the Royal United Services Institute (RUSI) think tank indicated.
Professor Malcolm Chalmers, the director-general of RUSI said the UK should embrace a new "special relationship" with the EU on foreign and security policy.
However, according to a report by the Times, that relationship could be entirely different.
Sources of the newspaper said that last autumn, Paris sent an unofficial delegation to Washington to lobby US officials, claiming that French armed forces were better placed than their British counterparts to be the US' special ally in Europe following Brexit.
The French team, including a naval captain and a senior official at the defence ministry, "were at pains to point out how useful the French military could be as an ally and their track record in getting things done in troublespots where the US was not as strong as it wished to be," said a source with knowledge of the September mission.
"They also pointed out that, after Brexit, they would be the only EU country with this capability."
Such a change would represent a significant loss of prestige for Britain, who has filled the second-in-command role almost continuously since 1951.
The role is currently held by General Sir Adrian Bradshaw who will hand over to Lieutenant-General Sir James Everard in March.
Sir Adam Thomson, who stepped down as Britain's ambassador to Nato in November, said he doubted that Britain would lose its deputy command status, but said it was likely that the EU element of the job would be stripped away.
"Politically, sticking with a Brit to command EU missions seems unlikely given Brexit," Thomson said.
A Ministry of Defence (MoD) spokesman said: "We will continue to play a leading role in European security. This includes providing Nato's deputy supreme allied commander for Europe."