It is seeking early contractor involvement (ECI) for the scheme, which also includes work to the Malpas Viaduct and Usk River Bridge.
The estimated value of the 20-month project is between £30m and £40m.
This project involves the delivery of significant structural protection and major improvements to life safety engineering systems in the tunnels.
The tunnels were damaged by a major lorry fire in 2011.
Further details of the tender in The Construction Index Contract Leads section.