Michel Barnier said a long extension to the UK’s current 12 April exit date carried “significant risks for the EU” and that a “strong justification would be needed” before the EU would agree.
Theresa May is set for five hours of cabinet talks to tackle the deadlock.
MPs rejected a customs union with the EU by three votes while a motion for another referendum got the most votes in favour, but still lost.
The so-called indicative votes were not legally binding, but they had been billed as the moment when Parliament might finally compromise.
That did not happen, however, and one Tory MP – Nick Boles, who was behind one of the proposals – resigned the whip in frustration.
Brexit Secretary Stephen Barclay told MPs that if they wanted to secure a further delay from the EU, the government must be able to put forward a “credible proposition” as to what it would do.
One suggestion has been the possibility of a general election – but former foreign secretary Boris Johnson told BBC political editor Laura Kuenssberg that would likely “infuriate” voters.
Instead, Mr Johnson said he believed a new leader and “change in negotiation tactic” could “retrofit” the PM’s “terrible” agreement with the EU.
Labour MP and chairman of the Brexit select committee Hilary Benn told BBC Radio 4’s Today that a confirmatory referendum was the best solution.
“A good leader would be taking that decision and put it back to the people,” he said.
“[The] fear is that the PM is not going to move an inch. That is why we are at a moment of crisis.”
Speaking on Tuesday morning, Mr Barnier said: “No deal was never our desire or intended scenario but the EU 27 is now prepared. It becomes day after day more likely.”
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Mrs May’s plan for the UK’s departure has been rejected by MPs three times.
Last week, Parliament took control of the process away from the government in order to hold a series of votes designed to find an alternative way forward.
Eight options were put to MPs, but none was able to command a majority, and on Monday night, a whittled down four were rejected too. They were:
Motion C: Committing the government to negotiating “a permanent and comprehensive UK-wide customs union with the EU” as part of any Brexit deal.
Motion D: Referred to as Common Market 2.0, this option would mean joining the European Free Trade Association and European Economic Area.
Motion E: Calling for a confirmatory referendum, giving the public a vote to approve any Brexit deal passed by Parliament before it can be implemented.
Motion G: Aiming to prevent the UK leaving without a deal, including a vote on whether to revoke Article 50 – stopping Brexit altogether – if the EU does not agree to an extension.
Those pushing for a customs union argued that their option was defeated by the narrowest margin – only three votes.