Final costings for the project have now been confirmed at £73m up from an initial estimate of £60m.
The rise in the final budget reflects updated costs for groundworks, construction prices and contingencies built-in by the council and the Birmingham 2022 Commonwealth Games budget.
Councillors are set to sign off funding and contract agreements at a meeting next week.
Work to prepare the site is already well advanced with the main building work set to start in January.

Architect Robert Limbrick designed the centre with Arup as structural and building services consultant
The world-class facility at Londonderry Lane in Smethwick will host the swimming and diving events at the Birmingham 2022 Commonwealth Games.
Sandwell Council will contribute £27m with £38.5m coming from the Birmingham 2022 Commonwealth Games budget.
A further £7.6m is funded by other external partners Sport England, Black Country LEP, Sandwell Leisure Trust (SLT) and University of Wolverhampton.
Sandwell Council had already budgeted to build a new leisure centre for Smethwick and can now provide a much bigger, improved facility at a similar cost to the authority – thanks to additional funding brought in by hosting the Commonwealth Games.
When complete, the centre will have a 50m Olympic-sized swimming pool, a 25m diving pool and a studio pool along with 1,000 permanent spectator seats. Additional seating will be added on a temporary basis for the Games.