The scheme consisting of six blocks up to 12-floors high is being brought forward by Warrington & Co, the council’s regeneration arm, and developer Altered Space.
Up to 215,000 sq ft of office and 11,000 sq ft of leisure and retail as well as a hotel is also planned for the site around Scotland Road.
The proposal involves the demolition of the current Cockhedge Shopping Park and the council office building called New Town House.
According to planning documents, the project is expected to cost around £100m to build, creating 160 on-site jobs during a 10-year build period.