Agreements are authorized between the department and any county, or counties, or city, or cities, providing for the acquisition of property for, the construction, improvement and maintenance of any highway, including those not in the State Highway System, and those lying partly within and partly without the boundaries of the State, to be constructed with federal aid. The department may, when authorized by any such written agreement, acquire for the county or city, as the case may be, any real property within the State required for any such highway which is not in the State Highway System.