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 nine 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.
Read MORE
BBC NEWS