The council hopes to have partner companies signed up in time to start the new contract on 1 August this year.
Its present partnership is with Alun Griffiths Contractors and Hanson Contracting.
Under the new deal, the winning firm would carry out general civil engineering, highways planned maintenance, improvement and new constructions works.
Further information can be obtained from: http://etenderwales.bravosolution.co.uk. Expressions of interest need to be in by 23 January.
The six highest scored firms from PQQs will be invited to submit their tenders in April.