Sky News and ITV both reported that the planned line between Birmingham and Manchester will not go ahead.
The prime minister and chancellor Jeremy Hunt have repeatedly refused to confirm that the project would be completed, amid concerns over soaring costs.
But ITV political editor Robert Peston said Sunak “has now taken the decision to shelve the Manchester leg”.
Writing on X, he said the billions of pounds saved will be spent on “other transport projects in the north”.
It is thought the PM could announce the decision when he makes his keynote speech to the Tory conference - which is coincidentally taking place in Manchester - on Wednesday.
But in a statement, a No.10 spokesperson said: “These reports are incorrect. No final decisions have been taken on phase 2 of HS2.
Speculation that HS2 could stop at Birmingham has sparked a furious backlash from business leaders, opposition politicians and senior Tories including Boris Johnson, George Osborne and West Midlands mayor Andy Street.
Speaking at an impromptu press conference outside the conference centre this afternoon, Street warned Sunak he will be “turning his back on a once in a generation opportunity to level up” in the UK.
He added: “You will be damaging our international reputation as a place to invest.”
Shadow transport secretary Louise Haigh said: “This fiasco shows the Conservatives are too divided, distracted and incompetent to take our country forward.
“After weeks of chaos and indecision on Europe’s biggest infrastructure project, this conference is showcasing why people can’t afford five more years of the Tories.”
Liberal Democrat transport spokesperson Wera Hobhouse said: “Rishi Sunak using a conference in Manchester to cancel the northern leg of HS2 would make Liz Truss look like a political genius.
“Yet again, a Conservative Party conference has become mired in chaos while the country suffers.”