Sajid Javid has decided to throw his support behind HS2 ahead of a key meeting with Boris Johnson on Thursday.
The chancellor is expected to tell the PM he supports the controversial London to Birmingham rail link after studying Treasury analysis of its impact on regional development and rail capacity.
A leaked report has suggested the project could cost almost double the £56bn originally expected in 2015.
Mr Johnson has said MPs can expect a decision “very shortly”.
No 10 said a final decision on the rail link would not be taken on Thursday – although the meeting, also involving Transport Secretary Grant Shapps, is expected to go a long way to coming up with a decision about whether to back the project
The BBC’s political editor Laura Kuenssberg said the mood music seemed to be pointing towards going ahead but massive anxieties remained.
She said senior government figures had suggested that cancelling the project at this stage would be a “credibility issue”.
The chancellor’s support for the project was first reported by the Financial Times, which said that he had concluded that alternatives to the scheme did not add up.
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.
The government commissioned a review into the line last August, designed, ministers said, to determine whether the project could still be deemed value for money.
Billions have already been spent on it, but Transport Secretary Grant Shapps has refused to rule out scrapping it entirely.
Mr Shapps 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The unpublished report, which was leaked to the FT, said there was “considerable risk” that estimated costs could rise by another 20% – but it did conclude that despite the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.
Mr Johnson faced calls to back HS2 from Conservative MPs at PMQs.
Kevin Hollinrake, MP for Thirsk and Malton, in North Yorkshire, called on the government to increase rail capacity “in and between the North, the Midlands, the South and Scotland”.
This could only be done by investing in the Midlands Engine, the Northern Powerhouse and carrying on with HS2, he told the PM.
Mr Johnson said the government was looking at investing into the North and Midlands and added that MPs could “expect an announcement very shortly” on HS2.
The PM also sought to reassure Paul Howell, freshly installed as Sedgefield’s new Conservative MP, who called for a “positive” decision to improve connectivity in his region.
Keiran Mullan, Tory MP for Crewe and Nantwich, urged the PM to “get HS2 done to secure jobs across the country”.
Speaking on Wednesday, the BBC’s political editor said the signs were that HS2 would get the go-ahead, even though there were very powerful voices critical of it high up in government.
She said it was in part a question of credibility – it would be difficult for a government that says it is committed to greater investment in the Midlands and North to cancel the biggest project on its books designed to do that.