The 100m long passenger tunnel will link the new Crossrail station to the London Underground Bakerloo Line station at Paddington.
London Underground has estimated the Paddington Bakerloo Line Link Project will cost £30-£55m to build.
Initially a shallow pedestrian walkway was planned but this carried the risk of damaging the railway station building.
An alternative, deeper level design for the link is now proposed, which falls outside of the original powers of the Crossrail Act
The preferred option is to place a temporary construction shaft at the junction of London Street and Winsland Mews.
TfL aims to prequalify firms able come up with innovative ideas to deliver significant cost reductions and optimise the programme.
Interested firms need to submit prequalification documents, which can be obtained from the TfL procurement portal, by 25 November.