The BBC understands “live discussions” are going on in No 10 about asking Parliament to approve a snap poll.
Political editor Laura Kuenssberg said it could happen as soon as Wednesday but no final decision had been taken.
Mr Johnson is due to make a statement in Downing Street at about 1800 BST setting out the choices facing MPs.
Tory ex-ministers are joining forces with Labour to stop the UK leaving the EU on 31 October without a deal.
Amid mounting speculation about an election, Mr Johnson is due to hold an unscheduled cabinet meeting at 17.00 BST and will also speak to the wider Conservative parliamentary party later.
The prime minister has said the UK must leave the EU on 31 October, with or without a deal, prompting a number of MPs to unite across party lines to try to prevent the UK leaving without an agreement.
They are expected to put forward legislation on Tuesday to stop no deal under “SO24” or Standing Order 24 – the rule allowing MPs to ask for a debate on a “specific and important matter that should have urgent consideration”.
Sources have told the BBC the bill would force the prime minister to seek a three-month extension until 31 January if no withdrawal deal has been passed by 19 October – the day after the next EU leaders’ summit.
Tory rebels – who include former ministers and prominent backbenchers – have been warned that those who support the legislation face being expelled from the party and deselected.
But leading figures, including ex-Justice Secretary David Gauke, have insisted that despite the threat, they will press ahead and – in their words – put the “national interest” ahead of their own.
Fellow rebel and former Chancellor Philip Hammond has written to Mr Johnson to ask for details about the state of negotiations with the EU and what alternatives to the Irish backstop – the major sticking point in the talks – his government has put forward.
A No 10 spokesman said it was treating this week’s Brexit votes as an issue of confidence – those traditionally trigger a general election if the government loses.
There is not scheduled to be another general election until 2022.
Under the terms of the Fixed Terms Parliament Act, Mr Johnson would require the backing of two-thirds of the UK’s 650 MPs to trigger an early poll this autumn.
Should this happen, the prime minister would be able to recommend the date – likely to be a hugely contentious issue – to the Queen.
Elections traditionally take place on a Thursday and, in law, 25 days have to elapse between the current Parliament being dissolved and the polls opening.
If MPs vote for an election this week and Parliament is dissolved on Thursday, the earliest date that could come into play is 10 October.
Those who back a negotiated Brexit deal, or want to remain in the EU, have been concerned the PM could delay the poll to the start of November, after the UK has left the EU, making it impossible to stop a no-deal Brexit.
Labour leader Jeremy Corbyn has said the UK “needs” a general election, as it “would give the people a choice between two very different directions for the country”.
He has dismissed warnings from former Labour leader Tony Blair, who said an early election was an “elephant trap”, and Mr Johnson could win such a vote as “some may fear a Corbyn premiership more” than a no-deal Brexit.
SNP leader Nicola Sturgeon said it was imperative any new government was elected before the UK’s departure.
If there is an election before the end of 2019, it would be the third in the past five years, after polls in 2015 and 2017.
Meanwhile, BBC Brussels correspondent Adam Fleming said the manoeuvrings in Westminster were not having much of an impact in Europe.
“All they really want to know is whether the UK is going to come forward with concrete proposals to deal with this issue of the backstop,” our correspondent said.
Mr Johnson wants the controversial Irish backstop – intended to avoid a hard border on the island of Ireland – scrapped, but the EU’s lead Brexit negotiator, Michel Barnier, has rejected this demand.
Meanwhile, the EU has said it is considering classifying a no-deal Brexit as a major disaster, like an earthquake, so countries worst affected could get access to more funding.
It’s more than just Westminster talk and rumours.
If rebels defeat the government and vote for another Brexit delay then No 10 is considering with utmost seriousness whether to push the button on a general election campaign.
The big question is whether or not the prime minister tries to have an election before we leave the EU – as the law currently stands – on 31 October.
The government could also put forward a date this week when they say they want to have a general election, but they could then change that date without having to have a vote from MPs.
Labour politicians would have very, very different views on what to do, but Jeremy Corbyn did seem to indicate he would back a general election.
It would be rather awkward for him not to, when he and senior Labour politicians have been calling for a general election for such a long time.
What could happen this week?
- Tuesday: MPs return to the Commons after their summer recess. Opposition MPs are expected to put forward legislation to stop no deal under “SO24” or Standing Order 24. This would be the bill’s first reading.
- Wednesday: In theory, the bill would then be debated and could potentially pass through all further Commons stages. However, the bill must pass through a series of votes and receive backing from more than half of MPs to pass to the next stage. Boris Johnson’s first PMQs as prime minister also takes place.
- Thursday: If MPs passed the bill, it could then reach the House of Lords by Thursday, but consideration of the bill could spill into Monday. It will be debated and voted on. The House is not due to sit on Friday.
- Monday, 9 September: If the bill passes these hurdles it could gain Royal Assent, formally making it law.
This could be a tight timetable as there are as few as four sitting days before Parliament is suspended. This is due to happen between Monday, 9 September, and Thursday, 12 September, under plans announced by the prime minister.
Another hurdle for any bill could come in the Lords. Although opponents to no deal have a large majority, peers wanting to block legislation could talk until there is no time left.