European Council president Donald Tusk is also favouring a longer extension, and ahead of tonight's summit in Brussels wrote to EU leaders asking for them to back a plan which could Brexit delayed for another year.
If EU leaders reject the Brexit delay proposal or don't go with Tusk's proposition for a long Brexit delay, Britain will leave the bloc without a deal at 11pm local time on Friday, 12 April.
Without a postponement, Britain is due to crash out of the European Union at midnight on Friday under a "no-deal" Brexit that could trigger economic chaos.
German Chancellor Angela Merkel has delivered a blow to UK PM Theresa May, after insisting a "longer" Brexit extension than the one asked for by the beleaguered Tory leader may be required.
Labour want to see the United Kingdom enter in a customs union with the EU after Brexit, but May has repeatedly said the government must be able to operate its own trade policy.
Environment Secretary Michael Gove said the talks had been "open and constructive" but the sides differed on a "number of areas".
May had come to the summit requesting a delay until June 30 but had acknowledged she would be willing to extend that date. "The question of non-participation could depend also on the British government", an European Union diplomat told the newspaper.
The depth of the anger within the Tory ranks was underlined by a Commons vote on Tuesday, when 97 Tory MPs voted against a motion backing Mrs May's call for an extension which only passed with the support of opposition MPs.
May is unlikely to object this condition for Brexit delay, and the United Kingdom will, therefore, remain without a representative in the European Commission for the first time since joining then-European Economic Community in 1973, The Guardian newspaper specified. And the EU27 would avoid repeated Brexit summits.
"This is why I believe we should also discuss an alternative, longer extension". Importantly, a long extension would provide more certainty and predictability by removing the threat of constantly shifting cliff-edge dates.
Mr Barclay, a Brexiteer, sidestepped questions as to whether Mrs May could remain in office if the European Union insisted on a longer delay.
"I don't think we should be rushing to change our leader when there is a big task to be done", he told BBC Radio 5 live.