One front runner, who wished to remain anonymous, confirmed he had been contacted to lead the scheme, and was told to "name his price", to lead the mega-project by recruitment head-hunters.
The candidate has not yet made up his mind, and NCE believes that he is one of a number in the frame to lead this mega-project.
Meanwhile, Arup director Mark Bostock this week said that megaprojects would be better served if promoted privately, rather then publicly.
Bostock is engaged in securing cash and planning to build a £4.5bn high speed rail link between St Pancras station and Heathrow airport, and to build a Heathrow “hub” which would give the airport unrivalled public transport links.
He told NCE: "I understood that the purpose of the private sector was efficiency – offsetting the higher costs of using private rather than government money.
"The private sector should be there in the driving seat and should be taking the appropriate risk."
Crossrail is promoted jointly by Transport for London (TfL) and the Department for Transport (DfT) – although the DfT will take a back-seat – and delivery company Cross London Rail Links will become a subsidiary of TfL in October.
Arup is bidding for the Crossrail Delivery Partner contract to manage the central London tunnelled sections as part of the "Flare" consortium, in addition to design frameworks.