Number 10 said the PM shares the public’s “frustration” at Parliament’s “failure to take a decision”.
EU Brexit negotiator Michel Barnier has 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.
Any delay will have to be agreed by all 27 EU member states and Mrs May is heading to Brussels on Thursday to discuss the options with fellow leaders.
It comes after 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 a third attempt at getting MPs to back the deal – but Speaker John Bercow effectively torpedoed that with his surprise intervention.
Explaining that Mrs May “won’t be asking for a long extension” when she writes to the EU, Number 10 said: “There is a case for giving Parliament a bit more time to agree a way forward, but the people of this country have been waiting nearly three years now.
“They are fed up with Parliament’s failure to take a decision and the PM shares their frustration”