British citizens should be able to choose to keep various benefits of EU membership including the freedom of movement after Brexit, the European Parliament's chief negotiator has said.
Guy Verhofstadt said he hoped to convince European leaders to allow Britons to keep certain rights if they apply for them on an individual basis.
He told BBC Radio 4's Today programme: "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."
But he also warned that the European Parliament will have veto powers and could reject any deal brokered between the UK and the European Commission.
He claimed to have received more than a thousand letters from UK citizens who do not want to lose their relationship with "European civilisation".
Mr Verhofstadt previously said the EU needs to be "open and generous" to individual UK citizens and said politicians were considering how to allow them to maintain their ties to the continent.
He told an audience at Chatham House in January: "We are scrutinising, thinking, debating how we could achieve that.
"That individual UK citizens would think their links with Europe are not broken."
Mr Verhofstadt warned that the European Parliament could veto any deal struck between the EU and the UK.
"We vote No - that is possible," he told Today. "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."
Mr Verhofstadt said the withdrawal negotiations would be "very complicated", and he was critical of the failure of the Remain campaign to make clear the uncertainties of Brexit during the referendum campaign.
"My feeling is, why is this only emerging now that there are all these difficulties?" he said.
"It would have been better maybe if all these difficulties emerged already at the moment of the referendum. I think the Remain campaign was only about economics and not about anything else."
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."
Mr Verhofstadt said he expected that, immediately after the triggering of Article 50, the Parliament will debate and vote on its "red lines" for the Brexit negotiations, such as the requirement for single market members to respect the "four freedoms" of movement of people, goods, services and capital.
"It will reiterate the necessity that a single market is linked to the four freedoms, the necessity that the customs union is linked to competence concerning trade agreements," he said.
"It will clearly indicate also that it is not possible to have better treatment outside the European Union than inside."
The first task of the negotiations will be to clarify the position of EU citizens living in the UK and Britons resident on the Continent, before moving on to discussing the size of the exit bill to be paid by Britain on withdrawal, he said.
Mr Verhofstadt said he expected it to be "possible to find agreement" on the bill despite the "enormous gap" between the 60 billion euro figure being discussed in Brussels and the suggestions of ministers like Boris Johnson that the UK should pay nothing.
But he cautioned against assumptions that a final settlement will simply split the difference between the two sides' initial positions.
"I don't know if it will be in the middle," he said. "There are objective facts in all this. You can find them in the budget of the European Union, controlled by the Court of Auditors."
Mr Verhofstadt said the withdrawal agreement needs to be completed by November or December 2017, in order to allow for a transition period to negotiate details of the future UK-EU relationship.
"Let's not be naive, it will not take two years," he said. "It will take two years plus the whole period of the transition to sort out this new partnership between the UK and EU."
He said it was vital to ensure that a final agreement preserves the soft border between Northern Ireland and the Republic.