In a letter to European Council president Donald Tusk on Wednesday, the Prime Minister is expected to ask for a three-month extension to June 30 in the hope of securing approval from MPs for her Withdrawal Agreement.
Tory tensions came to the fore at a fractious Cabinet discussion of the planned letter on Tuesday.
A Number 10 source said: "PM won't be asking for a long extension. 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.
Any request for extra time is subject to unanimous approval by leaders of the remaining 27 EU states at a meeting in Brussels on Thursday.
First Minister Nicola Sturgeon reacted to news, posting on Twitter: "The question is how long the so called moderates in her own party are going to allow this pandering to the hardliners to continue."
Liberal Democrat Brexit spokesperson Tom Brake said: "The Prime Minister blames parliament for not taking a decision. It has. Huge majorities of MPs have voted against her deal on two occasions.
"The country is not frustrated with parliament. It is frustrated with this weak Prime Minister, listless Government and the total mess the Conservatives have made out of Brexit."
European Commission president Jean-Claude Juncker said he had not received Mrs May's letter, but was hoping for "clarity" from the UK on the way forward.
He suggested that agreement on an extension to Article 50 might not be reached at this week's European Council summit, and that EU leaders might have to meet again next week to finalise it.
Speaking to German radio station DRF, Mr Juncker said: "We will probably have to meet again next week, because Mrs May has not got agreement for anything either in her Cabinet or her Parliament.
"As long as we don't know what Great Britain will say Yes to, we can't come to a resolution."
Mr Juncker said the EU had already moved a long way to accommodate the UK's demands, and there would be "no more negotiations".
"I am ready for any movement, but we have already moved intensively towards Britain," he said, adding: "There isn't any more."
Asked about indications from Downing Street that Mrs May will request a short extension, Mr Juncker told DRF: "Those months would have to produce, as an end result, an agreement from the British Parliament to the text which is before them."
"If that doesn't happen, and if Great Britain does not leave at the end of March, then we are, I am sorry to say, in the hands of God. And I think even God sometimes reaches a limit to his patience."
Commons Leader Andrea Leadsom, who is reported to have berated Cabinet colleagues in Tuesday's meeting, said the PM is "extremely frustrated" but "remains determined to take us out of the EU" and hopes to do so without participating in EU elections.
She told LBC: "It's absolutely essential we're out of the EU before the European elections. It would be extraordinary for the people who voted to leave the EU to find us fielding candidates for these next elections.
"She's absolutely working her socks off to get to that point so, in seeking a short extension, she and her Cabinet will be determined to get further progress on the meaningful vote so we can get her deal voted through in Parliament."
Education Secretary Damian Hinds said a short extension was the right choice.
He told the BBC's Today programme: "I don't see how a long delay gives certainty, actually, we've had a long time already. Unless and until a deal is finalised, there remains the prospect, the risk, of no deal.
"In terms of timing there has already been two-plus years to do this and I think people are a bit tired of waiting for Parliament to get our act together and get the deal passed."