The building's been shut ever since the Seddon earthquakes in 2013.
The project's now going to cost 112.4-million-dollars.
That's an increase of more than 20-million-dollars - since the most recent update on the project last year.
Naylor Love has been named as the preferred company for the job.
The four-year-project will start in March if councillors give it the go ahead at a meeting next week.