Former chief Brexit negotiator Michel Barnier has said the door "remains open" for the UK to rejoin the EU at any time.
The two sides should work together urgently to build a new partnership, including an agreement on defence and security co-operation, Mr Barnier said.
The bloc's negotiator said it was for the British people to decide if they wanted to rejoin the EU.
“It is not for me to give advice to say you have to join or not to join," Mr Barnier said. "It will be your choice, the choice of your leaders, the choice of your MPs.
"It will be your choice and your sovereign choice, exactly as Brexit has been the choice of the UK people.
“The door on the EU side will remain open any time ― for you and some others. If Switzerland or Norway were to change, the door is open. Everybody knows the conditions.”
Mr Barnier told an event organised by the UK In A Changing Europe think tank that even with the UK outside the EU, there are “so many reasons” to work together, from combating terrorism to tackling climate change.
At the same, he said he believed there was a willingness on both sides to resolve the differences over the Northern Ireland Protocol, which could pave the way for progress on other issues.
“We have a solid and competent prime minister with Mr [Rishi] Sunak," Mr Barnier said.
"It would be a common interest as urgently as possible to build this new partnership between the UK and the EU."
“We can open discussion for a new agreement on defence matters in addition to the bilateral co-operation between France and the UK and Germany and the UK, and complementary to what we are doing in the Nato framework. No question.
“There are many fields we can improve and build this kind of partnership. There is a certain number of challenges we can only face together.
"Even if your country is now outside of the EU, we must co-operate to exist.”