Sadiq Khan will strike an optimistic tone in a speech on Wednesday night about the prospect of the High Speed 2 rail line reaching Euston.

Speaking at the London Transport Museum’s annual dinner and auction, the mayor is expected to say it is “looking increasingly positive” that the multi-billion pound railway will terminate in the city centre, rather than at Old Oak Common.

It comes after the Sunday Times reported last week that the Chancellor, Rachel Reeves, is preparing to approve plans for the required 4.5-mile tunnel link and for an overhaul of Euston station itself.

A Government source told the newspaper: “HS2 just wouldn’t work if the terminus was not at Euston. The station is also well overdue for investment and has become a dystopian mess and a stain on London.”

The question of whether HS2 would reach Euston became less certain in October last year, when the then-PM Rishi Sunak announced that the link from Old Oak Common and the construction of a new station at Euston – together estimated to cost £4.8bn, having ballooned from an original budget of £2.6bn – would instead be built using private finance.

But Sir John Armitt, chair of the National Infrastructure Commission, poured cold water on the proposal, saying that the Government will still “need to be ready to fund the core civil engineering” works.

In his speech, Mr Khan will say: “In my first two terms as mayor, it would’ve been unthinkable to call a minister, pitch an idea and for them to then approve it.

“But this government – not yet three months old – has already consented to our plans to build 350 new homes at Cockfosters station and to breathe new life into Oxford Street.

“And while I don’t want to tempt fate, it’s looking increasingly positive that HS2 will come to Euston. This – for me – is but a glimpse of the London we can build.”

If Ms Reeves does back the Euston link in her upcoming Budget, it remains unclear whether the Government will 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.

The mayor will on Wednesday however reiterate his promise to use his position “to lobby for more transport investment in our city”, including the extension of the DLR to Thamesmead, the opening of the West London Orbital rail line and the Bakerloo line extension to Lewisham and beyond.

Realising those projects will be partly dependent on Transport for London (TfL) securing a long-term funding deal, which Mr Khan says is necessary “to give us the capacity to reach for the future once again”.

The mayor’s speech will come on the eve of his Thursday trip – with Transport Secretary Louise Haigh – to Goole, Yorkshire, where Siemens Mobility will start building modernised Piccadilly line trains at a new facility there.

“It’s a project that’ll create up to 700 direct jobs and a further 1,700 in the supply chain,” Mr Khan will say.

“Let us not forget that our new Piccadilly line fleet is just one example of the enormous and enduring contribution TfL makes to our wider economy and society.

“Our investment means businesses of all sizes in every corner of our nation can grow. In turn, more workers are provided dignity and security through meaningful jobs.

“When London builds, Britain benefits. It’s a basic formula, but it works.

“And it’s the one I’ll be putting to ministers tomorrow – and every day after – on behalf of TfL, our friends in industry and all Londoners as we seek to kickstart a new era of strong and sustainable growth across our country.”

The mayor will also pledge to “protect the Crossrail 2 route, so the grand project to link north and south London can be realised one day” and will hail his plans to create a second Superloop network of express bus routes.