The second phase, taking the line in a Y-shape to north-west and north-east England, is set for completion around 2032/33.
Launching his report in Manchester, Sir David will say that he would like work to start on the second phase at the same time as the first phase.
He is also expected to recommend a completely new station at Euston, the site for the line's London terminus.
Sir David, the former London Olympics supremo who has joined HS2 Ltd after being Network Rail chief executive, is also expected to recommend scrapping plans to link HS2 with HS1, the London to Kent coast Channel Tunnel high-speed line.
HS2 is facing a number of obstacles over and above strong opposition by residents who face years of disruption while the building work goes on.
Mr Balls is not the only Labour politician to express reservations about the scheme. Former chancellor Alistair Darling and former industry secretary Lord Mandelson have also questioned the project's viability.
In addition, Transport Secretary Patrick McLoughlin has said that the legislation for phase one of the project will not get through Parliament before next year's general election.