Martin Selmayr, Secretary-General of the European Commission, made the jaw-dropping offer over a private lunch with Theresa May’s deputy in summer 2018.
The deputy, David Lidington, said Mr Selmayr claimed he could put Brexit on hold for five years and propose a “new deal for Europe”.
Cabinet Office Minister Mr Lidington told BBC Panorama: “Martin sort of said ‘look, why don’t we have a deal whereby we just put all this on ice for five years.
“‘Let’s see how things go, let’s get the UK involved with France and Germany, let’s see how the dust settles and let’s talk about whether we can come to a new deal for Europe’”.
Asked if he was tempted to explore the offer further, Mr Lidington said: “I said, ‘look we’ve had a referendum.
“Practically all of us in Parliament said we were going to accept the result of that referendum whether it went our way or not.
“And that matters in British democratic politics and I don’t think there can be going back on that.”
Nicknamed the “monster”, Professor Dr Martin Selmayr is the powerful chief of staff to Jean-Claude Juncker – though he recently revealed he will be standing down as his boss is replaced by German minister Ursula von der Leyen.
The 46-year-old German lawyer, who claims to speak seven languages, acted as the European Commission President’s enforcer in his bid keep the EU united during Brexit.
Some blamed him for a leak in 2017 that claimed Theresa May had a “disastrous” dinner with Mr Juncker – claims Mrs May branded “Brussels gossip”.
And when Commission Vice-President Kristalina Georgieva quit last year, she declared: “The combination with Martin Selmayr is just poisonous.” He insisted they had “good relations”.
Mr Selmayr was interviewed for the Panorama show and said he is “very certain” the UK is unprepared for No Deal Brexit .
“We have seen what has been prepared on our side of the border for a hard Brexit,” he said.
“We don’t see the same level of preparation on the other side of the border.”
The EU’s chief Brexit negotiator, Michel Barnier, claimed Theresa May never even once threatened him with a No Deal Brexit.
Mr Barnier told Panorama: “I never listened to such a sentence. Never.
“I think that the UK side… knew from the very beginning that we’ve never been impressed by such a threat. It’s not useful to use it.”
Boris Johnson has now declared he will massively ramp up planning for No Deal Brexit “from the get go” once he becomes Prime Minister next Wednesday.
The Tory leadership frontrunner said Britain needs to “make sure everybody understands all the possible risks” of crashing out of the EU without agreement on October 31.