Officials on the £15.9bn project are currently drawing-up plans to save cash as part of the government’s austerity drive.
But budgeting options are not believed to include dropping major stations like Tottenham Court Road or Bond Street or cutting part of the route which extends to Canary Wharf.
One source said: “It hardly makes sense to build a new route but not major stations along it – where would people get on and off?
“There is already a rather large hole at Tottenham Court Road where the station works are taking place and the same goes for Canary Wharf.
“This will be more of a value engineering exercise and reports that £5bn could be cut look well wide of the mark – that is nearly a third of the project cost.”
A TfL spokesperson said: “This story is just pure speculation.
“The Mayor and TfL, alongside London’s business community, continue to make the case for investment in London’s transport infrastructure, including the delivery of Crossrail and the Tube upgrades in full, which are so vital to the future economic growth and development of London and the UK.
“The funding package for Crossrail balances the cost of construction between fare and taxpayers and private business.
“£5bn of the total £15.9bn funding package comes from Government in the form of a grant from the DfT. Much of the funding comes from borrowing against future fare revenue and levies on business.
“Any delay to the project would actually increase costs. The DfT and TfL continue to work to deliver Crossrail with the best possible value for money.”