Brexit could be delayed until 2021 under plans being explored by the EU’s most senior officials, at a time of growing exasperation over Theresa May’s handling of the talks, the Guardian can reveal.

A lengthy extension of the negotiating period is gaining traction as the EU’s default position should the Commons continue to reject May’s deal, and a request emerge.

Replacing the 21-month transition period with extra time as a member state would allow the UK and the EU to develop their plans for the future relationship with the aim of making the contentious Irish backstop redundant.

Theresa May's Brexit vote delay: what does it all mean? Read more

Brussels is determined to avoid offering a short extension only to have to revisit the issue in the summer when the government again fails to win round parliament.

“If leaders see any purpose in extending, which is not a certainty given the situation in the UK, they will not do a rolling cliff-edge but go long to ensure a decent period to solve the outstanding issues or batten down the hatches,” one EU diplomat said.

“A 21-month extension makes sense as it would cover the multi-financial framework [the EU’s budget period] and make things easier. Provided leaders are not completely down with Brexit fatigue, and a three-month technical extension won’t cut it, I would expect a 21-month kick [of the can]. It is doing the rounds in Brussels corridors. Martin Selmayr [the European commission’s secretary-general], among others, also fond of the idea.”

Exasperation with May’s handling of Brexit is growing in Brussels as senior insiders put the chance of the UK crashing out without a deal at “more than 50%”.

Informed sources say there is dismay that senior government figures are focused on seeking domestic political advantage and appear wilfully blind to the opposition to reopening the withdrawal agreement.

One insider said there was concern that there was no domestic consensus over the withdrawal agreement but also over the UK’s position on what kind of trading relationship it wanted when the transition period elapsed.

“Some say: ‘We can have Norway, we can have Canada, we can have a customs union, we can’t have a customs union. Some of them say we are not to be trusted because they think we are going to use the backstop to keep them in the EU forever, but if you look at the confusion, you can see precisely why the backstop is necessary,” said an insider.

There is also disquiet that Ireland will be scapegoated for no deal when member states believe the country is being used as a proxy to tease out positions on future trade talks. For this reason “any attempt to blame the Irish for no deal will backfire,” said a source.

There is also bewilderment that the recent flurry of meetings in Brussels involving May’s Brexit secretary, Stephen Barclay, and the attorney general, Geoffrey Cox, are being characterised in London as “negotiations” when the reality is the EU is still waiting for the prime minister to show them the alternative arrangements for the Irish backstop for which she claims to have a majority in support.

The frustration being felt in Brussels was evident after Cox arrived in Brussels with no concrete proposals. “We are still in wait-and-see mode. There is a feeling that Britain is overplaying how things are going,” said an insider.

One senior EU diplomat said May was to blame for failing to confront hardline Eurosceptic Tories. “She gave the impression that you can stay in your delusional comfort zone, but you can’t,” the diplomat said. “Unless she is ready to choose there is nothing we can do.”

Facebook Twitter Pinterest Theresa May hopes to reassure Brexiters of the temporary nature of the Irish backstop. Photograph: Mohamed Abd El Ghany/Reuters

Concerns emerged as May flew in to the Red Sea resort of Sharm el-Sheik for an EU-Arab league of states summit on Sunday, and confirmed she would not be putting a revised Brexit deal to the Commons this week. Even so she insisted that it “within our our grasp to leave the EU by 29 March and that is what we are planning to do”.

May said she would instead put the deal to parliament on 12 March and brushed off the calls by three cabinet ministers – Amber Rudd, David Gauke and Greg Clark – for a no-deal scenario to be ruled out.

“What we see around the cabinet table are strong views on the issue of Europe,” she said. “What we are doing as a government is ensuring we are doing everything we can to leave the European Union with a deal.

“People are talking about the extension of article 50 as if it solves the issue when of course it won’t. It defers the point of decision. There comes a point when we must make that decision.”

There is growing support, however, among MPs for an amendment due to be tabled this week by the former Labour and Conservative cabinet ministers Yvette Cooper and Oliver Letwin, which would instruct May to seek an extension of article 50 if she does not have a deal ratified by 13 March.

As he arrived at the summit in Egypt, Sebastian Kurz, the Austrian chancellor, offered his support for a delay to Brexit given the impasse in the negotiations.

“If by the beginning of March there’s no support for the deal then I think it would be good to postpone Brexit because a no-deal scenario is bad for the EU but extremely bad for the UK,” Kurz told reporters.

EU officials are understood to be looking at options if such an extension request is received: a three-month “technical” extension to allow extra time for ratification if the parliamentary process develops positively, or a longer prolongation of nine to 21 months should there be no clear way to break the current impasse.

A source close to the European council president, Donald Tusk, said that as a request had yet to be made by Downing Street, the issue had not been discussed by leaders. “No Tusk position on this,” the official said of the mooted 21-month extension. “At this stage, at least.”

But sources said the EU was determined to avoid a series of three-month extension requests by the UK, which would cause damaging uncertainty, leaving Brussels unable to plan for the future.

The emergence of the idea of a 21-month delay to Brexit will be seen by some as an attempt to push Brexiter MPs into backing May’s deal.

The EU’s chief negotiator, Michel Barner, had advised ambassadors last week that the threat of a lengthy extension could be used by May as leverage in talks with her Brexiter MPs as she seeks to nudge the deal through parliament.

May is meanwhile driving on with seeking legally binding changes to the withdrawal agreement to reassure Brexiters of the temporary nature of the Irish backstop, which would keep the UK in a customs union to avoid a hard border on the island of Ireland.

The prime minister updated Tusk during a 30-minute meeting at the summit in Egypt on her plans for the meaningful vote. “No tensions,” an EU source said. “Focus on practicalities.”

Tusk was said to have told May that the EU would have “clarity that a proposal for the way forward can command a majority in the UK, before the issue is tackled by the European council”.

The Irish taoiseach, Leo Varadkar, who will hold talks with May on Monday in Egypt, dismissed claims made earlier on Sunday by Michael Gove, the environment secretary, that a time limit or unilateral exit mechanism from the Irish backstop could still emerge from the talks.

“A backstop that includes a time-limit is not a backstop at all. Nor would a unilateral exit clause work for us,” Varadkar said.