Sajid Javid has decided to throw his support behind HS2 ahead of a key meeting with Boris Johnson later.
The chancellor is expected to tell the PM he supports the controversial London to Birmingham rail link after studying Treasury analysis of its impact, as first reported by the Financial Times.
A leaked report has suggested the project could cost almost double the official 2015 estimate of £56bn.
Transport Secretary Grant Shapps said the HS2 decision would come next month.
No 10 said the meeting, also involving Mr Shapps, was expected to go a long way towards reaching a verdict.
BBC political editor Laura Kuenssberg said the mood music seemed to be pointing towards going ahead but massive anxieties remained.
Senior government figures had suggested that cancelling the project at this stage would be a “credibility issue”, she added.
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During Transport Questions in the Commons on Thursday, Mr Shapps said MPs “won’t have to wait very long” to hear a decision on HS2, adding: “We will have an announcement on this next month.”
Mr Shapps also defended the right of Conservative MPs to oppose HS2, following growing criticism of the project from a number of them.
In response to Labour MP for Chesterfield Toby Perkins, who urged the government to “get control” of MPs “who are constantly undermining” HS2, Mr Shapps said they were entitled to represent the views of their constituents.
He added that the project should be properly debated.
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Phase 1 of the rail line between London and Birmingham is due to open at the end of 2026, with the second phase to Leeds and Manchester scheduled for completion by 2032-33.
It is designed to carry trains capable of travelling at 250mph (402km/h).
The government commissioned a review into HS2 last August, designed, ministers said, to determine whether the project could still be deemed value for money.
Billions of pounds have already been spent on it, but Mr Shapps has refused to rule out scrapping it entirely.
He revealed last week he had asked for more data before making a “massive decision” on HS2, after a leaked government review found it could cost £106bn.
The unpublished report, which was seen by the Financial Times, said there was “considerable risk” that estimated costs could rise by another 20% – but it did conclude that despite the ballooning bill, it should still go ahead.
The government previously promised to make a decision on HS2 before the end of 2019.
Several Tory MPs have criticised the project, including Tory MP for Buckingham Greg Smith, who told BBC Radio 4’s Today programme that he and others would be ready to vote against the government.
“It is absolutely wrong for my constituents,” he said, “and I believe it to be wrong for the country as well and I made very clear commitments in the general election that come what may I will oppose HS2.”
In the Commons on Thursday, Philip Davies, Tory MP for Shipley, called HS2 a “catastrophic waste of money”.
He said “better infrastructure” was needed in the North and West Yorkshire and he asked about the government’s intended timetable for completing Northern Powerhouse Rail (NPR).
The NPR project was part of Mr Johnson’s wider commitment to deliver a high-speed railway link across the north of England.
But Labour MP Mr Perkins urged the government to commit to HS2, calling it “the most important infrastructure project this country has”.
And the prime minister also faced calls to back HS2 from Conservative MPs at Prime Minister’s Questions on Wednesday.