It is not yet clear whether Labour has made headway in attracting the private financing that the Conservatives had made a prerequisite for the Euston expansion, which is expected to cost billions of pounds.
However, a Government source said Ms Reeves was likely to approve the Euston extension without finalising the financing arrangements. Without private backing, it will be down to the taxpayer to foot the bill.
As part of any Euston expansion, the Government must also decide whether to retain Mr Sunak’s slimmed-down plans for a six-platform HS2 terminus or reinstate the original blueprint for an 11-platform layout, with a new Tube station.
Labour has been under pressure to make a swift decision on the Euston leg after two 1,700-tonne boring machines were delivered from Germany last month. The company responsible for overseeing HS2 has warned that the machines cannot be left underground indefinitely and that drilling must begin early next year.
Louise Haigh, the Transport Secretary, earlier this month told the Evening Standard that HS2 would never have been built solely to link Birmingham with Old Oak Common.
She said: “Clearly Euston is going to be part of the wider picture but we will be making a decision soon on the tunnelling and the development.”
Separately, Ms Reeves is also thought to be preparing to approve a new rail link between Liverpool and Manchester that would run via Manchester airport.
A Government spokesman declined to comment.