Click here to see a map of the route
The rail link will run through tunnels in central London stopping at key Tube stations such as Bond Street, Tottenham Court Road and Liverpool Street.
Discussions about how much funding will come from taxpayers are thought to be ongoing.
The government will need to create a hybrid bill for the scheme, combining both a public and a private bill, in other words it mixes legislation applying equally to a group of people with legislation applying to specific individuals or companies.
The scheme has long been a top priority of London Mayor Ken Livingstone.
Earlier this month Mr Livingstone set out his plan for the way the city's transport system should look by 2016, with Crossrail at the top of the list.
He said the project would increase rail capacity in London by a fifth.
The Crossrail spokesman said on Monday: "If we are going to get an announcement tomorrow, then it's really good news."
"The idea of a cross-London rail link has been kicking around for decades.
"We will need to carry out more work before a hybrid Bill can start
going through Parliament and the scheme would not be ready before 2013 at the
But Lynne Featherstone, the Liberal Democrat's spokesman for transport on the London Assembly, said the announcement still failed to say who would cover the cost of the project.