The draft proposals also include a plan for a larger green zone to be introduced in 2021/22, covering the rest of the city centre.
If agreed, the charging scheme for the red zone, pictured, would be in force from 7am to 7pm. Only zero-emission vehicles would be exempt, with a daily charge of £10 for all other vehicles, rising to £20 by December 2024.
Bus operators would not be affected, as they have already agreed timelines for zero-emission fleets across the city.
An informal consultation is underway, with the councils seeking feedback on charging, proposed discounts and hours of operation.
A formal consultation on the red zone will begin in March, with a final decision in the spring.
If the ZEZ is expanded to cover the green zone in 2021/22, this scheme would have separate requirements, including a discounted charge for low-emission Euro VI vehicles.