Philip Hammond is set to warn that a no-deal Brexit would harm the British economy, devour a £26.6bn Brexit war chest, and risk the break-up of the UK.
The chancellor is expected to say that Conservative candidates who are vying to be the next prime minister must come up with a Brexit plan "B".
If they do not, he will hint that a second referendum could be needed to break the Parliamentary deadlock.
He will also pour cold water on tax and spending pledges by the candidates.
Mr Hammond is set to say in a speech at the annual Mansion House dinner in the City of London on Thursday that a no-deal Brexit would soak up £26.6bn that has been set aside that could otherwise be spent by an incoming prime minister.
In a BBC debate on Tuesday, leadership candidates promised tax cuts and increased spending on public services.
However, a no-deal Brexit would mean that was not possible, and would also leave the UK economy "permanently smaller", Mr Hammond will say.
In March, the chancellor pledged to spend the war chest to boost the economy, if MPs voted to leave the European Union with a deal.
Conservative candidates including Boris Johnson have pledged to leave the EU by 31 October, even if that means quitting without a deal.
But a no-deal Brexit would "risk the Union", Mr Hammond is expected to say.
"I cannot imagine a Conservative and Unionist-led government, actively pursuing a no-deal Brexit; willing to risk the Union and our economic prosperity," he will say.
Scottish Tory leader Ruth Davidson told party members on Tuesday to "take a long, hard look at themselves" after a YouGov survey suggested 63% would back Brexit even if it meant Scotland leaving the UK.
In April, Scotland's First Minister Nicola Sturgeon said she would push for a second referendum on Scottish independence by 2021 if the country, which voted Remain, is taken out of the EU.
'Tell the truth'
Mr Hammond is also expected to say that certain "truths" will not change no matter who is leader.
Unless there is a general election, Parliament will not support a no-deal, and is unlikely to support the deal that has already been negotiated, he will say.
So candidates need to spell out their "Plan B", he is expected to argue.
The EU will not renegotiate Theresa May's Brexit deal, and the problem of the Irish border "will not go away", Mr Hammond will add, saying that Tory leadership candidates "need to be honest with the public".
The chancellor will also caution the men vying to lead his party that they have to "recognise and address the difficult trade-offs inherent in delivering Brexit".
Candidates will also need to say how they will bring about Brexit without harming the economy or breaking up the UK, he will say.
The leadership contenders "need realistic strategies for taking the UK economy out of the holding pattern in which it has been stuck for the last nine months and landing it safely on the runway marked 'prosperity Brexit'".
"If the new prime minister cannot end the deadlock in Parliament, then he will have to explore other democratic mechanisms to break the impasse," Mr Hammond will add, hinting at a second referendum, or even a general election.
However, Mr Hammond's expected speech was "yet another example of how far the Tories are cut off from the real world," said Labour's shadow chancellor John McDonnell.
"Hammond's austerity policies have resulted in a near decade of suffering for hungry children, a surge in food bank use, rising in-work poverty, squeezed incomes for families and unprecedented cutbacks to public services," he said.