BBC political editor Laura Kuenssberg said senior sources had told her it was "inconceivable" the prime minister could remain in office if MPs rejected her Brexit plans for a fourth time.
Theresa May and Jeremy Corbyn have clashed following the collapse of cross-party talks aimed at finding a Brexit compromise.
The cross-party talks between May's Conservative Party lawmakers and socialist firebrand Jeremy Corbyn's Labour always seemed a long shot, but May resorted to opening the talks after Parliament overwhelmingly rejected the agreement she thrashed out previous year with European leaders on three separate occasions.
The Labour leader pulled the plug on negotiations after six weeks of talks, saying they had "gone as far as they can" and "we have been unable to bridge important policy gaps between us". Labour has feared that any compromises on issues such as workers' rights would be torn up by May's successor.
And when told: "It's a matter of transparency", the politician replies: "It certainly is, we have got a democratic election next Thursday which is all about democracy and you won't even talk about it".
She says that if it passes, Britain could leave the European Union in July, well before the October deadline set by the bloc.
Johnson quit as foreign minister past year over the government's Brexit strategy and has been an outspoken critic of the divorce deal May struck with Brussels last November.
But the Conservatives and left-of-centre Labour differ on how close an economic relationship to seek with the bloc after the United Kingdom leaves.
The decision comes as little surprise as Johnson, one of Britain's most identifiable politicians known simply as "Boris", has always been known to covet the top job.
That deadlock deepened this week with the breakdown of the cross-party talks and the intensifying pressure on Mrs May from within her Conservative Party to quit. Many blame May for the impasse and want her replaced with a more staunchly pro-Brexit leader such as the former Foreign Secretary, Boris Johnson.
That will trigger a potentially brutal Conservative leadership contest, with Boris Johnson, Sajid Javid and Jeremy Hunt among the contenders.
May's deal has faced opposition from those who wish Britain was remaining in the European Union and want a second referendum, as well as those on the right of her party who believes that it leaves Britain handcuffed to the bloc.
May announced this week that she will put her Brexit deal back to a vote in Parliament in the week of June 3, but it's not clear she would have the support she needs.
Referencing those developments, Corbyn wrote that, "the position of the government has become ever more unstable and its authority eroded" stating the party would continue to oppose May's deal.
Following disastrous results in the English local elections and European Parliament election polls indicating that the Tories have slumped to just 9 per cent public support, the Prime Minister has reportedly been forced to agree she resign by the end of June by the infamous "men in grey suits".
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