Top EU officials are seriously considering delaying Brexit until 2021 as Brussels grows increasingly exasperated by the UK's handling of the matter, the Guardian reported on Sunday. 

The plans, which would see the March deadline extended by a further two years, are reportedly favoured by EU Council president Donald Tusk and EU Commission secretary-general Martin Selmayr.

The Guardian quoted unnamed senior EU officials as saying they were unwilling to consider a short-term extension, fearing that would just delay ongoing problems by a few months, but were more receptive to a two-year moratorium. 

Reports of the EU's plans came just hours after UK Prime Minister Theresa May sparked outrage by suggesting parliament may not be able to vote on her Brexit deal until March 12, just days before Britain is set to leave the EU.

The decision increases the chances that MPs will themselves move to delay Brexit beyond March 29, to avoid a potentially disastrous situation where Britain exits with no agreement at all.

May had held out the possibility of a vote this week, but said Sunday she was still discussing with the EU possible amendments to the deal's arrangements for the Irish border.

"As we're continuing with those talks, we won't bring a meaningful vote to parliament this week," she told reporters as she arrived at a summit of European and Arab leaders in Egypt.

"But that will happen by March 12. And we still have it within our grasp to leave the European Union with a deal on March 29."

Since MPs rejected her withdrawal deal last month, May has sought to address their concerns about the text's "backstop" arrangement, which is designed to keep the border with Ireland free flowing.

She is meeting with European Council chief Donald Tusk and German Chancellor Angela Merkel at the two-day summit in Sharm el-Sheikh, and her team will also return to Brussels on Tuesday.

But opposition politicians and pro-European MPs in London reacted with fury at what they believe is a deliberate strategy of delay.

Labour's Brexit spokesman Keir Starmer said her move not to hold a vote this week was "the height of irresponsibility and an admission of failure".

"Theresa May is recklessly running down the clock in a desperate attempt to force MPs to choose between her deal and no deal," he said.

"Parliament cannot stand by and allow this to happen."

'Run out of road' 

May has refused to rule out leaving the EU with no deal, despite the risk of huge economic disruption on both sides of the Channel.

She says the only way to avoid this scenario is to support her deal -- but growing numbers of MPs believe that Brexit should instead be delayed.

Three of her cabinet ministers on Saturday warned in a newspaper article that if there was no breakthrough this week then the House of Commons would vote for a delay.

"Beyond the next few days, there simply will not be time to agree a deal and complete all the necessary legislation before March 29," they wrote.

May has promised to make a statement in the Commons on Tuesday and allow MPs on Wednesday to debate their own ideas for the way forward.

Labour MP Yvette Cooper urged lawmakers to support her cross-party proposal to delay Brexit, saying: "How are businesses, public services and families supposed to plan in this chaos?"

Sam Gyimah, who quit as a junior minister in May's government over her approach to Brexit, said her latest decision was "shocking".

"We've run out of road. The meaningful vote can is now being kicked against the wall," he tweeted.

'Addition to the treaty'

After rejecting the EU withdrawal deal that May spent almost two years negotiating, MPs demanded she return seek changes to the Irish backstop.

This plan would keep Britain in a customs union with the EU after Brexit if and until another way -- for example, a free trade deal -- were found to keep open the border with Ireland.

The EU has said it will not reopen the text, but is looking at what "guarantees" could be given to reassure MPs that the backstop would be temporary.

Earlier, Environment Secretary Michael Gove said the government was still discussing various options.

"It could be a time limit, it could be a unilateral exit mechanism," he told the BBC -- citing two options Brussels has publicly rejected.

He added: "And it could be another legally powerful protocol or addition to the treaty that makes it clear that we would not be bound in the backstop indefinitely against our will."