The council wants to build a 12,000-seat arena next to Temple Meads station. It is aiming for completion by June 2017.
It calculates that £38m of the cost would be met by rent paid by the venue operator. The remaining £35m would be sought from the City Deal Economic Development Fund, managed by the West of England Local Enterprise Partnership
The arena funding package will go to full council on 18 February as part of the council’s budget proposals.
Mayor George Ferguson said: “We know that there is a ready audience to come to Bristol to see performances and we know that there are operators keen to run the arena for us but we also know that arenas cannot be built without some public subsidy.”