The highways service contract could be extended to the full 12-year term, estimated to be worth up to £800m.
The job involves major projects, routine planned and cyclical road maintenance and streetlighting, although the council hopes to remove lighting from the contract if it can find alternative funding.
Design and construction of bridges is also included in the scope of works.
PQQs need to be returned to Martin Jaques in the environment department by 13 September.
Highways maintenance in the region is presently being carried out by AmeyLafarge and consultant Mouchel.
Last year the original contract was extended to 2012.