European Council president Donald Tusk believes delaying Brexit is a "rational solution" - although Theresa May has pushed back at suggestions the UK could seek an extension to Article 50.
Speaking at an EU summit with Arab leaders on Monday, Mr Tusk revealed he and the prime minister have discussed "the legal and procedural context of a potential extension" to the UK's period for negotiating its EU exit.
Article 50 is the clause of an EU treaty which triggered the UK's withdrawal from the EU - giving it two years to negotiate an exit deal.
Following the overwhelming rejection of Mrs May's EU withdrawal agreement by the MPs last month, Mr Tusk noted there is "no majority in the House of Commons to approve a deal".
The Brussels official claimed, in the continued absence of MPs approving a deal and with just 32 days until the UK's scheduled departure, the "alternative" will be "a chaotic Brexit or an extension".
"The less time there is until 29 March the greater the likelihood of an extension," he added.
"This is an objective fact, not our intention, not our plan but an objective fact.
"I believe in the situation we are in an extension would be a rational solution."
However, Mr Tusk did note Mrs May "believes she is still able to avoid" extending Article 50, with the prime minister herself also dampening expectations of a delay to Brexit.
Despite not ruling out the possibility of extending Article 50, Mrs May claimed "it is within our grasp to leave with a deal on 29 March", adding: "That's where all of my energies are going to be focused."
Speaking shortly after Mr Tusk at a news conference at the summit in Sharm el Sheikh, Egypt, the prime minister continued: "An extension to Article 50, a delay in this process, doesn't deliver a decision in parliament, it doesn't deliver a deal.
"All it does is precisely what the word 'delay' says. Any extension of Article 50 isn't addressing the issues."
Mrs May also said she had gained a "real sense" from her conversations with EU leaders at the summit - and in the days before - "that we can achieve that deal".
A Conservative minister has told Sky News that if Mrs May does not have a deal by 13 March, she should extend Article 50 to avoid a no-deal Brexit.
The warning comes after three ministers - Amber Rudd, Greg Clarke and David Gauke - signalled they were willing to back moves to delay Brexit.
The prime minister is currently battling to win "legally-binding changes" to the backstop arrangement within her Brexit deal.
The backstop is aimed at preventing a hard border on the island of Ireland, in the event such a scenario is not averted by a future EU-UK trade relationship.
But many MPs fear it could leave the UK permanently trapped in a customs union with the EU.
Downing Street confirmed on Monday the prime minister is still aiming to reopen her withdrawal agreement with the EU, despite repeated opposition from Brussels to renegotiating the terms of her Brexit deal.
Mrs May has promised to hold another meaningful vote in the House of Commons on her revised Brexit deal by 12 March, but intriguingly raised the prospect of MPs voting on her altered withdrawal agreement before it had been signed off by EU leaders.
Asked whether EU leaders need to approve a revised deal before there is a meaningful vote in parliament, or whether parliament can vote for a deal before EU leaders approve it, the prime minister replied: "It is possible to do it either way."
The next scheduled European Council summit of EU leaders is on 21 March, little more than a week before the UK's supposed exit from the bloc.
Mrs May was also revealed to have discussed a possible extension to Article 50 with German chancellor Angela Merkel while in Sharm el Sheikh.
However, a senior UK government official stressed the issue was mentioned only "fleetingly", with it suggested Mrs Merkel was the one to raise the subject.
Irish prime minister Leo Varadkar said he had "confidence" the UK would not "crash out" of the EU without a deal.
"We'll either have a deal or we'll have an extension," he said.