Chris Bolt has given the team, which includes Balfour Beatty and WS Atkins, a deadline of October 12 to present its case in the row over extra costs during maintenance work.
He said: “I will then make a final decision on November 12 but Metronet will receive between £340 million and £1 billion from London Underground.”
Mr Bolt has given LU, which insists it owes Metronet nothing, the same date to respond. He added: “LU has always maintained it will pay zero.”
Metronet went into administration over the summer claiming it was owed closer to £2 billion. Ernst & Young was appointed administrator.
A Transport for London spokesman, whose responsibilities include LU, said: “What we find so bizarre is why he is continuing this exercise outside the formal extraordinary review. The administrator hasn’t asked him to.”
London mayor Ken Livingstone wants TfL to take over Metronet’s responsibilities for maintaining and upgrading the Tube.