Prime Minister Theresa May is writing to the EU to formally ask for Brexit to be postponed.
One ministerial source told the BBC the longer delay could be up to two years, amid reports of a cabinet row, but No 10 said no decision had been made.
EU Brexit negotiator Michel Barnier said the EU would not grant a delay without a “concrete plan” from the UK about what they would do with it.
Under current law the UK will leave the EU with or without a deal in 10 days.
MPs rejected the withdrawal deal Mrs May has negotiated with the EU 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 deal this week – but Speaker John Bercow effectively torpedoed that with his surprise intervention on Monday.
She still hopes to ultimately get it in front of MPs for a third go, but says even if that happens and they vote in favour of it, the UK will need a short extension to get the necessary legislation through Parliament.
A cabinet source told the BBC she therefore plans to ask the EU to agree to postpone the UK’s departure until 30 June, but with an option of a longer delay as well.
Mrs May has warned Brexiteer Tories that longer extension will be needed if her deal does not get through Parliament.