The Sun reported that instead of running to Euston, trains would stop at a new interchange at Old Oak Common in the west London suburbs, meaning commuters would have to end their journey on the Tube.
The initial estimate for the second leg of the project from Birmingham to Manchester was £26 billion. This was expected to rise to nearly £40bn, according to research from last year.
Some critics have previously called on the government to scrap the entire above-cost project.
MPs have argued that the total cost estimate, of between £72bn and £98bn, cannot be justified at a time of economic uncertainty when the government has raised the tax burden to its highest level in decades.
The estimate is calculated in 2019 prices and does not take into account the effect of recent inflation. Unofficial calculations based on headline inflation from the CPI suggest that the real cost will exceed £100bn.
Asked whether the leg to Euston might be scrapped, a Department for Transport spokesperson told The Sun: “The government remains committed to delivering HS2 to Manchester, as confirmed in the autumn statement.”
Henri Murison, chief executive of the Northern Powerhouse Partnership, said a London terminus for HS2 would need to be “centrally located” following reports the rail infrastructure project could end in a western suburb of the capital.
He added: “I think there are ways to deal with the current inflationary pressures.
“I don’t think the government shouldn’t be addressing that pressure on public spending, but it was incredibly short-term to take a project for decades and take it apart to solve an accounting problem because it is essentially an accounting problem.
“Because ultimately the benefits of this UK PLC will still far outweigh the benefits, but if we keep cutting it fundamentally, we won’t get anywhere near the transformational change that the whole of the UK was promised.”
He continued: “I believe Manchester will still draw its line, but my argument would be that I’m interested in what’s good for the whole of the UK.
“And actually, even for the north of England, not going to Euston has some significant drawbacks.
“Because people in the north of England, people in Birmingham, want to access central London – that’s what they currently have through the normal main network.
“These stations must be centrally located.”