The other options were the no-deal Brexit or a long delay of the UK's leaving date.
After the UK Parliament once againrejected alternative options to Prime Minister Theresa May's Brexit deal, European politicians were quick to react. The U.K. has until April 12 to determine next steps, with more votes planned next week.
On the day the country was originally scheduled to leave the EU, March 29, MPs voted down May's deal with the bloc for the third time.
Obviously it would be nearly a slam dunk for Theresa May if the DUP's 10 MPs could cease their opposition to the Withdrawal Agreement - maybe there is still a way for the DUP to aid the PM's dunking.
"During any long extension, there will be no renegotiation of the Brexit withdrawal agreement, no, never", Barnier told an audience at the European Policy Centre event.
The cross-party talks offer has angered politicians including Boris Johnson, accusing ministers of "entrusting the final handling of Brexit to Labour".
The group said it would be up to the government to decide how long to propose as a delay.
Labour Party: Given the lack of support within the governing parties, May needed opposition backing for her deal.
Making her offer to Mr Corbyn she said the "ideal outcome" would be to agree an approach to the future relationship that both leaders could back and which she could then take to her 27 European Union counterparts at a summit next week.
EU chief negotiator Michel Barnier says that Britain's exit from the European Union without a deal "becomes day after day more likely" after the United Kingdom parliament again rejected alternatives to the government's unpopular divorce deal.
"What is missing is an answer to the question that many MPs faced up to last night - what is the compromise she is willing to make?"
No-deal: Parliament did not support leaving with no deal.
Theresa May can not ignore backing for a "softer" Brexit.
Two proposals to keep Britain in a customs union with the EU narrowly missed on a majority, while a proposal of a second referendum also came up short.
The ideas considered by MPs included a plan to hold a confirmatory referendum and the option to remain in the European Union's single market, but none of the plans gained a majority. An amendment to his motion would set aside April 8 for indicative votes.
Any meeting with Corbyn will likely require one or both of them to shift on their red lines, with analysis after her statement suggesting that May may be willing to do so on the subject of the customs union, an option that Labour backed during Monday's House of Commons vote. We can not, legally speaking, negotiate with a member state about future relations.