Theresa May is writing to the EU to ask for Brexit to be postponed until 30 June with the option of a longer delay, cabinet sources say.
One minister told the BBC’s Laura Kuenssberg there was “no agreement” around the cabinet table.
Another source expressed frustration that the prime minister did not make a clear indication of the option she would actually argue for.
Under current law the UK will leave the EU with or without a deal in 10 days.
The prime minister says the UK will need a short extension to get the necessary legislation through Parliament, if MPs back her withdrawal deal.
She has warned Brexiteer Tories a longer extension will be needed if the deal does not get through Parliament – but any delay will have to be agreed by all 27 EU member states.
Downing Street sources said there was no final decision at cabinet on the length of an extension.
Mrs May is heading to Brussels on Thursday to discuss the delay options with EU leaders.
Commons leader Andrea Leadsom is said to have criticised her cabinet colleagues, saying it is now a “Remain cabinet”, not a “Brexit Cabinet”, Laura Kuenssberg said.
Meanwhile, Taoiseach (Irish PM) Leo Varadkar and European Council president Donald Tusk released a joint statement after their meeting in Dublin.
“President Tusk expressed the strong and ongoing solidarity with Ireland of the European Council and European leaders,” their statement said.
“They agreed that we must now see what proposals emerge from London in advance of the European Council meeting in Brussels on Thursday.”
MPs rejected Theresa May’s deal for a second time last week by 149 votes. They also voted in favour of ruling out leaving the EU without a deal, and in favour of extending the Brexit process.
The prime minister had hoped to have another try at getting MPs to back the withdrawal deal she has agreed with the EU this week – but Speaker Bercow effectively torpedoed that with his surprise intervention on Monday.
He said he would not allow a third “meaningful vote” in the coming days on “substantially the same” motion as MPs rejected last week.
But Brexit Secretary Stephen Barclay suggested a vote could take place next week – after Mrs May has sought a delay to Brexit from the EU.
He said it was important to “respect the referee” and abide by his decisions – but, he added, Mr Bercow himself had said, in the past, that if Parliament was guided only by precedent then “nothing ever would change”.