Theresa May is facing growing calls to say she would delay Brexit rather than leave the EU if no deal is in place by the end of March.
A new plan from some Tory MPs suggests ministers postpone Brexit until 23 May “to conclude negotiations”.
It is being suggested as an alternative to cross-party proposals which would see MPs take control of the process.
Dutch PM Mark Rutte warned Mrs May the UK was “sleepwalking into a no-deal scenario” and needed to “wake up”.
The pair met at a summit in Egypt, as she presses EU leaders for more concessions to her deal.
Mr Rutte told the BBC: “It’s four weeks until the end date and still the UK has not agreed a position. So now we are sleep walking into a no-deal scenario.
“It’s unacceptable and your best friends have to warn you. Wake up. This is real. Come to a conclusion and close the deal.”
Mrs May announced on Sunday that MPs will get a fresh vote on her deal by 12 March, vowing that leaving as planned 17 days later was “within our grasp”.
But many MPs had wanted another so-called “meaningful vote” sooner than that, and Labour leader Jeremy Corbyn suggested Mrs May was “running down the clock” until a time when MPs were forced “to choose between her bad deal and a disastrous no deal”.
Mrs May’s announcement also provoked disappointment among business leaders, who are clamouring for certainty about what is to come.
The prime minister had a “good, friendly” 45-minute meeting with German Chancellor Angela Merkel on the sidelines of the EU-League of Arab States summit in Sharm-el-Sheikh.
A government official said they discussed Brexit, among other things, and the issue of extending Article 50 came up “fleetingly”. But they said Mrs May reiterated that the UK wanted to leave the EU with a deal on the scheduled date of 29 March.
European Commission president Jean-Claude Juncker also met the PM and said they had a “good, constructive” meeting.
There will be further talks in Brussels on Tuesday on the Northern Ireland backstop – the number one sticking point for many when it comes to the Brexit deal.
The prime minister has long resisted any suggestion that the UK’s departure could be postponed beyond 29 March.
But political editor Laura Kuenssberg says two cabinet ministers have told the BBC they believe she will this week grant some kind of concession to allow for a possible delay.
Such a move, though, would inevitably anger Brexiteers who want the UK to leave as planned, whatever the cost.
On Wednesday, MPs will get another chance to put forward a range of amendments in the Commons to show what direction they want Brexit to take.
One – drawn up by Labour’s Yvette Cooper and Conservative Oliver Letwin – would, if passed, give MPs the power to demand a delay to Brexit if a deal cannot be agreed by 13 March.
Three cabinet ministers, Greg Clark, Amber Rudd and David Gauke, signalled they could be prepared to vote for it if there is no breakthrough in the next few days.
Ms Cooper told the BBC that the move was not intended to stop Brexit as it would be up to the government, not Parliament, to determine the length of any delay.
Ms Rudd told reporters on Monday morning that she was “completely committed” to making sure the UK leaves the EU and she supported the prime minister.
But, she added: “What I don’t think is acceptable is plans to move ever closer to no deal.”