While council staff are uncertain how many firms will be selected for the framework, they are looking to bidders to suggest ideas for how a partnership would work.
Council procurement legal officer Rachel Hill said: "We are going out to the market and asking them what they can do for us. We are looking at new forms of contractual arrangement."
The council decided to move to a partnering framework following the conclusions of a best-value study conducted by council officers.
Deadline for expressions of interest is the end of October. A longlist of firms is unlikely to be drawn up until next February.
In the recent advertisement, the council said: "The successful organisations will be those whose values and work culture complement those of the authority – embracing customer focus and with a commitment to quality, sustainability and continuous improvement."
The council's construction work is divided into several areas. About 40% of capital expenditure is in housing, 20% is in education, 10% in social services and 10% in community facilities. Museums, libraries and civic buildings make up the rest.