Jean Claude Juncker has said he would be "happy" to help Britain rejoin the European Union if it wants to after Brexit.
The European Commission president said the UK could apply to rejoin under Article 49 of the Lisbon Treaty even after it leaves the EU in March 2019 - if the Government or British people want to "find a way out" of Brexit.
It comes after European Council president Donald Tusk said on Tuesday he was open to a "change of heart" from the UK.
Mr Juncker described Brexit as a "lose-lose situation" for Britain and the EU and a "catastrophe".
And addressing the European Parliament in Strasbourg on Wednesday, he went on: "Mr Tusk said that our hand remains outstretched.
"The British people, the British Government, may wish to find a different way out of the Brexit situation and we are very much willing to deal with them.
"We are not throwing the British out, we would like the British to stay, and if they so wish, they should be allowed to do so.
"In London, there was a rather irritated response to this proposal (to stay in the EU), but note that even if the British leave according to Article 50 then Article 49 would allow them to accede again and I would be happy to facilitate that."
Mr Juncker and Mr Tusk’s overtures came as a commission paper suggested the EU is toughening its stance on the transition period after the official date of Brexit on March 29 2019.
A document obtained by Brussels reporters suggests chief negotiator Michel Barnier wants free movement of people to continue throughout the period, and permanent rights to settle for any EU nationals moving to the UK before the end of 2020.
He is also set to insist that the UK will have to seek "authorisation" from Brussels to continue enjoying the benefits of the bloc’s existing trade agreements with non-EU countries, the paper suggests.
The December European Council had agreed that "sufficient progress" had been made on the first phase of Brexit talks, allowing negotiations to move on to consider transition and a future deal.
Labour MP Chuka Umunna said Britons have a right to change their mind about Brexit.
A year on from Theresa May’s Lancaster House speech setting out her negotiating priorities, Mr Umunna said on behalf of the Open Britain campaign for close ties with the EU: "Brexit is proving to be far more costly and complicated than we were led to believe.
"The promises made by the Prime Minister last January are today as worthless as a degree certificate from Trump University.
"In fact, talks on the future relationship with the EU haven’t even begun. She and her shambolic Cabinet cannot even agree what they want.
"A year on from Lancaster House, the Prime Minister must accept that Brexit on the terms it was sold is not possible, and be honest with people about the huge trade-offs ahead. Given what is at stake, everyone is right to keep an open mind about Brexit."
Meanwhile in Britain, the Brexit Bill was set to clear its final stages in the House of Commons on Wednesday.
The Prime Minister has already suffered one defeat on the European Union (Withdrawal) Bill at the hands of MPs but faces even tougher battles when the legislation enters the Lords.