Sir David Higgins proposed an accelerated timetable for phase 2 - the northern section of the high-speed line.
The former London Olympics guru also called for a new look at ways of improving connections between phase 2 and the existing railway.
And he proposed a larger development at Euston - the project's southern terminus - but said plans to link HS2 with HS1, the London to Kent Channel Tunnel high-speed rail link, should be reconsidered.
No government has yet made a commitment to extend the line to Scotland but a study aiming to increase the benefits to Scotland of the project was announced by the UK government last year.
Phase one would see a line running from London through Tory heartlands to Birmingham and is due for completion in 2026.
Phase two will see the line continue in a Y-shape from Birmingham to north-west and north-east England and, under current plans, would be completed around 2032/33.
The current total cost, including contingencies, is £42.6 billion, with £7.5 billion for the trains.
Shadow chancellor Ed Balls and others are concerned about the cost of the project but shadow transport secretary Mary Creagh welcomed yesterday's announcements.
She said: "We will continue to hold the Government to account for keeping costs down on the project."