Work involves expanding the station and adding a new ticket hall on Marylebone Lane, new escalators and a new low-level link between the Central and Jubilee lines.
The project includes providing a step-free link to the planned Crossrail station to be built alongside the existing station, and is expected to transform the Bond Street area to attract investment.
TfL expects the bids to be submitted by April and the contracts to be awarded by summer.
Construction is expected to begin by the end of the year and finish by early 2017.
The £16bn ($26m) Crossrail project, expected to be finished by 2017, will see a 72-mile rail route starting from Maidenhead in Berkshire to Heathrow Airport via central London to Shenfield in Essex.