The president of the European Commission made the suggestion as he entered a meeting with the heads of government of the other 27 EU states as they prepared to discuss Brexit
But leading Tory MEP Daniel Hannan said that Mr Juncker appeared to have missed the point about the whole referendum and how Britain wanted rid of him and Brussels rule.
He tweeted: “That’s kinda what the whole referendum thing was about.”
Mr Juncker said Theresa May had not briefed him on the Chequers meeting of her Brexit “war cabinet” when ministers agreed a broad policy for the next stage of negotiations, on trade.
He then quipped: “I am not the British prime minister. It would be good for Britain if I was, but I’m not.”
His comments came amid reports in the Belgian press that Mr Juncker and his Brexit chief negotiator Michel Barnier are on the verge of a humiliating climbdown.
It is suggested they will try for an ambitious deal previously attempted with America rather than the more limited deal agreed with Canada and favoured by Mr Barnier.
The American-style deal had proposals for free trade with financial services.
Tory MEP David Campbell Bannerman said: “This is good news. They seem to finally be coming round to reason.
“This means we can diverge from the EU economically and through regulations but have a free trade deal that is good for everyone.”
Mr Barnier had previously insisted that financial services could not be part of a final trade deal between the UK and EU.