The future of the controversial line, which is due to pass through Staffordshire, has come under the microscope of late due to concerns that it may not meet its £56bn budget.
According to the Financial Times, Allan Cook, the new chairman of HS2 Ltd, has written to the Department for Transport (DfT) warning that the scheme could cost £85bn – almost treble its initial budget from 2010.
It has prompted Labour to double down on its calls for a review into the costs of the line, while the Stop HS2 campaign group said the figure could even warrant a police probe.
Joe Rukin, from Stop HS2, said: "A potential £30bn cost hike will be of no surprise to anyone who has witnessed this project lurch from one disaster to another.
"We had been telling HS2 Ltd for years ground conditions would hike up the costs, but they chose not to do those surveys until the project had been passed.
"Worse than that, it seems that only after a decade of planning are they realising that building a railway for ultra-high speed trains costs more than building one for normal trains."
He said it was "beyond all credibility" that the potential cost over-run had appeared in the last eight months, suggesting that the public and parliamentarians may have been "deliberately misled to try and force this boondoggle upon us".
"This project has to be abandoned immediately, and we believe it is time to call the police in to see if fraud by abuse of position has taken place," he added.
"At the very least a full scale independent inquiry must now be called.”
Labour's shadow transport secretary Andy McDonald said the letter showed why an inquiry was needed, claiming that while additional rail capacity was required, it should not be built without a peer review.
"It is clear that the Government and HS2 have a lot of work to do if they're to restore confidence in this project," he added.
Boris Johnson has already pledged to review of the project, following a report by the House of Lords Economic Affairs Committee which questioned the economic case for the line.
A DfT spokesman said: "The chairman of HS2 Ltd is conducting detailed work into of the costs and schedule of the project to ensure it delivers benefits to passengers, the economy and represents value for money for the taxpayer.
"This work is ongoing. We expect Allan Cook to provide his final assessment in due course." HS2 Ltd said it did not comment on speculation, while HS2 Minister Nusrat Ghani has insisted the project will be completed to budget.