Engineers and designers have been asked to find significant savings on the route as part of the government’s cost-cutting drive.
Savings already identified include a complete redesign of Whitechapel station which has pruned £30m from the budget and a scaling down of Canary Wharf station.
The London Evening Standard said possible delays to the opening could be caused by a combination of redesign work and the previous timetable being “over ambitious”.
Insiders told the paper the opening date could be put back from 2017 to 2018.
Terry Morgan, Crossrail Chairman said: “Crossrail is bearing down on its whole cost base, while ensuring delivery of a new railway that is fit for purpose and delivers the capacity improvements required.
“We are looking at every aspect of Crossrail to identify where efficiencies can be made and understanding what cost saving lessons can be learned from other global infrastructure projects.”