Sunak's finance minister Jeremy Hunt fuelled speculation about the fate of the northern section of the HS2 line last month when he warned costs were "getting totally out of control" and refused to say whether it might be axed.
Several British newspapers and other media outlets reported Tuesday that the decision had been made to abandon the leg between Birmingham and Manchester.
The increasingly controversial infrastructure project was originally intended to link London with Birmingham in central England and other northern cities.
It would be only the UK's second high-speed railway after the one leading to the Channel Tunnel, linking England's southeast with northern France.
HS2 has already been pared back, with an eastern leg towards Nottingham scrapped in 2021.
In November that year a section supposed to link Birmingham with Leeds was also ditched, infuriating local politicians who accused the government of reneging on promises to disadvantaged regions of the north.
Estimated at £37.5 billion ($46 billion) in 2013, the cost has since soared to around £100 billion or possibly more.
Refusing to be drawn on the reports that he was about to scrap the Birmingham to Manchester route, Sunak said the expense of HS2 had gone "far beyond" what had been predicted.
"I know there's lots of speculation on it but what I would say is... the sums involved are enormous and it's right that the prime minister takes proper care over it," Sunak told Times Radio.
"It's taxpayers' money and we should make the right decisions on these things."
Cancelling the northern leg would be a damaging blow to the UK's reputation for delivering major infrastructure projects.
And politically it could leave Sunak's government open to accusations of abandoning the Conservatives' much-touted "levelling up" policy.
It aims to reduce economic inequalities across the country, including between the north and the more prosperous London-centred south.
Alongside Brexit, it was a key promise of the Tories' 2019 general election campaign, helping them to secure a landslide win in former heartlands of the main opposition Labour party across northern England.
At the party conference in Manchester on Monday, Conservative mayor of the West Midlands Andy Street made an impassioned last-ditch appeal to Sunak not to cancel HS2's northern section.
"You will be turning your back on an opportunity to level up -- a once-in-a-generation opportunity," he told reporters.
"You will indeed be damaging your international reputation as a place to invest," he said, adding he did not rule out resigning over the issue.
Work on the first section of HS2 between London and Birmingham began in April 2020, with the first trains due to run between 2029 and 2033.
The Labour mayor of Greater Manchester, Andy Burnham, said cancelling the link would leave people in northern England "second class citizens".
"If they're about to pull the plug, that would just be a desperate act of a dying government with nowhere left to go," he said.
The Conservatives, in power since 2010, are holding what could be their last annual conference before an expected general election next year.
Labour is well ahead in opinion polls amid the worst cost-of-living crisis in a generation, stubbornly high inflation and widespread industrial unrest.
Sunak is widely expected to make an announcement about HS2 in his conference speech on Wednesday, with speculation he could unveil new funding for east-west rail connectivity in northern England.
Opinions at the event on the project differed Tuesday.
"East to west is what we need -- a lot of people up my way have been saying that for a long time," said lifelong Conservative member Yvonne Peacock, 71, from North Yorkshire.
"If you want to level up the north, that's how you do it."
But Manchester resident Kathryn Morley, 61, representing a youth charity at the conference, said axing HS2's northern leg felt "like a bereavement".
"It's the symbolism as well as the practicalities," she told AFP. "If it does go, it's lost forever really as it's only going to get more expensive and difficult in the future."