'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.
Juncker's comments come just a day after European Council president Donald Tusk told Britain:'Our hearts are still open to you'.
Juncker told the lawmakers that "we are not throwing the British out".
But the official denied it was a ploy to divide the British side in the tough Brexit negotiations, saying: "Whatever Tusk might dream it doesn't influence how he will negotiate, which is based on a 99.9 percent assumption that the United Kingdom will leave".
Britain could take part in a new model of European cooperation after Brexit but is unlikely to rejoin the EU in its current form, a senior minister said Friday.
He noted that Britain will remain part of the North Atlantic Treaty Organisation military alliance, the Organization for Security and Co-operation in Europe, and the Council of Europe human rights watchdog.
However, May's spokesman said on Tuesday that there was no question of not following through in March next year on the referendum vote of June 2016 to leave the EU. "We want to agree [with the EU] on a comprehensive free trade agreement, as well as on a partnership in the field of security".
Constitutional lawyers are divided on whether Britain can withdraw its two-year notice to quit but the exchanges underline a view in Brussels that an EU political consensus could be found to avert Brexit - even if most are now resigned to Britain leaving and believe the Union will weather the disruption.
"I can't predict sitting here today what that network of organisations and alliances, including the European Union and how that will have changed, is going to look like in 10 years or 20 years times", he said.
'The promises made by the Prime Minister last January are today as worthless as a degree certificate from Trump University. She and her shambolic Cabinet can not even agree what they want'.