Despite rumours of a potential delay of either two months or two years swirling around like a sand storm in the nearby desert, the British prime minister was standing firm, head ducked down into the ground.

Repeatedly asked by reporters if she will consider extending the self-imposed deadline at a media briefing after separately meeting European Council president Donald Tusk, Taoiseach Leo Varadkar and German chancellor Angela Merkel, Ms May was clear in her public view.

No. Nil. Nein. This lady is not for turning, or at least surfacing, she explained again and again.

A "delay is a delay", she said when asked if any extension will be considered.

Everything can still be sorted out between March 12 and the current deadline of March 29, she explained to unconvinced onlookers aware of the difficulty of meeting such a plan.

"We still have it [leaving on March 29] in our grasp," she repeatedly insisted.

It's not the full story, and there is a sneaking suspicion that despite Ms May's public comments, she knows it.

Across the corridor to Ms May's briefing room moments before she took to the stage, European Council president Donald Tusk was giving a briefing of his own.

Standing between European Commission president Jean-Claude Juncker and Egyptian president Abdel Fattah al-Sisi, Mr Tusk was asked about rumours of a Brexit deadline extension.

He smiled, said he wanted to "put an end to the speculation" and then with one subtle slip, let the cat out of the bag.

At a private meeting on Sunday between him and Ms May, the British prime minister had asked him about the technical realities of a Brexit extension, should one hypothetically be requested in the future.

"I believe in the situation we are in it is a rational solution," Mr Tusk said, before adding it is not Ms May's "objective" and that she continues to be in opposition to such a move.

Similarly, at his own media briefing earlier in the day before he had met Ms May, Taoiseach Leo Varadkar said despite the ongoing threat of a no deal crash out Brexit, he is "confident" come March 29 there will either be an agreement or a delay.

Describing any alternative as "a lose-lose-lose scenario for everyone", he said there is a "sense the UK will not crash out of the EU without a deal on March 29, we will either have a deal or we will have an extension".

The comments from Mr Tusk and Mr Varadkar clash with Ms May's ongoing public insistence all her energies are on ensuring Britain leaves on March 29, a view she repeated during a private meeting with Ms Merkel on Monday.

However, with the British prime minister due to give an update statement to the House of Commons on Tuesday, a potential vote on the Yvette Cooper motion to take a no deal off the table on Wednesday, and British officials travelling to Brussels on Tuesday for further technical talks, all might not be quite what it seems.

A two year delay is almost certain to be rejected by hard-line Brexiteers as treason against the pro-leave voters in June 2016.

But a two or three month extension, provided it is used to good effect, could buy Ms May and the EU just enough time to avoid catastrophe.

The British prime minister is insistent nothing could be further from her mind as she continues to burrow down into the Egyptian sand. However, after 20 months of little to no progress, even she knows everything you have to come up to face the light.