Patrick McLoughlin said there would be up to seven construction teams on Phase 2 - the ‘Y’ route north of Birmingham - and one of them could start in Leeds.
It would head south and potentially link other parts of Yorkshire to high speed rail earlier than planned.
Speaking to The Star newspaper in Sheffield, Mr McLoughlin also addressed fears the £55bn scheme could be axed due to a post-Brexit decline in the country’s fortunes.
He said the high speed rail project was set to cost about £3bn-a-year over 20 years - compared to £700bn-a-year total government spending.
The MP for the Derbyshire Dales, said: “I don’t know why some people think it’s not going to happen. We’re making good progress with London to Birmingham. I believe HS2 will be completed as stated. £2bn-a-year is not a huge proportion of government annual expenditure and it’s very important for the future of the country. Fortunately the Prime Minister and Chancellor ‘get’ the importance of infrastructure in creating jobs and opportunities.”
London to Birmingham would be operating in 10 years, he added. “Then we should be looking at options for Phase Two, including construction in Leeds and Warwickshire at the same time, we will have up to seven different teams on it.”
Last week, Doncaster’s executive mayor criticised “last minute” changes to the route the proposed HS2 rail line will take through South Yorkshire.
Ros Jones expressed shock at HS2’s decision to move the path of the line significantly to the east of its original planned route.
The line was originally supposed to snake between Rotherham and Sheffield, stopping at a new station at the Meadowhall shopping centre.
Under new plans the Meadowhall station has been scrapped and the line will now pass between Rotherham and Doncaster.
Mr McLoughlin said the way the new route “ties in with Leeds and gives a stop at Chesterfield has positives”.