Guy Verhofstadt, a member of the Brussels negotiating team on Brexit, suggested that British citizens could be allowed to apply to keep some EU membership on an individual basis after the country leaves the bloc.
And European Commission President Jean Claude-Juncker signalled that looser ties to Brussels could be on offer in order to keep the UK on board the European project.
He said: “The day will come when the British will re-enter the boat, I hope.”
But the double hint of some form of associate membership of the EU for Britain was dismissed by Brexit campaigners as a cynical bid to “muddy the waters” ahead of the looming departure negotiations.
Mr Verhofstadt and Mr Juncker spoke out days before Theresa May is expected to trigger the EU’s Article 50 exit clause.
With the parliamentary debate over her powers to formally start the departure process due to be concluded at the beginning of next week, it is thought the Prime Minister could take the historic step as early as next Tuesday.
Mr Verhofstadt, the European Parliament’s lead Brexit negotiator, struck an emollient tone on the forthcoming talks in a BBC Radio 4 interview.
He called Britain’s exit from the EU “a tragedy” and said he wanted individual UK citizens to have the chance to retain membership if they wished.
He told the BBC: “All British citizens today have also EU citizenship.
“That means a number of things: the possibility to participate in the European elections, the freedom of travel without problem inside the union.
“We need to have an arrangement in which this arrangement can continue for those citizens who on an individual basis are requesting it.”
Mr Verhofstadt, a former prime minister of Belgium, claimed to have received more than a thousand letters from UK citizens who do not want to lose their relationship with “European civilisation”.
He also warned that the European Parliament could veto a trade deal between Britain and the EU if MEPs did not like the details of the agreement.
He said: “We vote No – that is possible.
“It has happened in a number of other cases that a big international multilateral agreement was voted down by the European Parliament after it was concluded.
“The fact that in the Treaty it is stated we have to say Yes or No doesn’t mean that automatically we vote Yes.”
Britain’s departure was “a crisis for the European Union”, he said.
“That Britain goes out of the European Union is, in my opinion, a tragedy, a disaster, a catastrophe.
“But it gives us also a responsibility to look for a new partnership between the UK and the European Union.”
He expected it to be “possible to find agreement” on the size of the UK’s divorce bill despite the “enormous gap” between the £52billion figure being discussed in Brussels and the insistence of senior ministers that Britain should not pay an exit fee.
Later, Mr Juncker also sounded a readiness to find a compromise deal for Britain’s future relationship with Brussels as he wrapped up a summit of EU leaders in Brussels yesterday.
He said: “I don’t like Brexit because I would like to be in the same boat as the British.
“The day will come when the British will re-enter the boat, I hope.
“But Brexit is not the end of the European Union, nor the end of all our developments, nor the end of our continental ambitions.”
A senior EU official explained that Mr Juncker’s offer could mean a return to full membership or a looser arrangement in an offer “that will always be open”.
He said: “There are different ways you can join.
“You can be a full member, you can be a partner, you can be related to us in the customs union, or through a trade agreement.”
Euro-sceptics last night warned that the offers would undermine the Government’s promise to end uncontrolled migration from the EU.
Richard Tice, co-chairman of the Brexit-backing pressure group Leave Means Leave, said: “If the EU wants to offer this to British citizens than that is a matter for them however Mr Verhofstadt underestimates the patriotism held by most British people.
“He makes no mention of the fee they would charge.
“In truth this is probably a cleverly disguised way of muddying the water and trying to dilute Brexit.
“The British people voted to get back control of their borders and ending freedom of movement from the EU is core to delivering on this.”
Nigel Farage said Mr Verhofstadt’s suggestion was “divisive and wrong”.
The former Ukip leader said: “Guy Verhofstadt is using European nationalism to try to destroy the nation state.”
And in response to Mr Juncker’s suggestion that the UK could “re-enter” the EU boat, Mr Farage insisted the vessel was “sunk”.
Downing Street officials dismissed Mr Verhofstadt’s idea of EU membership for individual EU citizens.
The Prime Minister’s spokesman said: “It’s not something that we have ever proposed or said that we are looking at.
“We will go into negotiations and discuss the ideas put forward by the EU and its various institutions.
Alp Mehmet, vice-chairman of Migration Watch UK, said: “If Mr Verhofstadt is proposing that British nationals be given some sort of free movement rights, almost certainly that will require some sort of treaty.
“It just doesn’t make sense – which makes me think he’s just saying it to be mischievous.”
March 10th, 2017: Express