The agency is introducing “Free Flow” tolls at the crossing in a bid to cut congestion.
The contract involves changing the road layout at the site and the design,build and operation of a new tolling system for the 43m vehicles which use the crossing every year.
The tender race for a separate civils package worth £75m was started last month.
Any new system would use number plate recognition to allow vehicles to use the crossing without having to stop at traditional toll gates.
The contract includes a massive software and back-office toll collection operation and will run for at least eight years.
The agency is looking for a single contractor or a consortium to deliver the scheme.
Firms must express an interest in the job by October 29 with Highways Agency Lateral, 8 City Walk http://highways.bravosolution.co.uk George Crawshaw LS11 9AT Leeds UNITED KINGDOM +44 1132835893 firstname.lastname@example.org