A petition for an extension to parking at Russell Street, which can be used by permit-holders only, was submitted at full council on June 23.
It called for land on Bright Street, at the bottom of the car park, to be converted into extra parking spaces.
A total of 56 signatures were gathered before the petition closed on July 7.
In a response to the petition dated July 15, the city council property team said it looked further into the potential of the project.
The land in question, said chartered estates surveyor Sarah Cracknell, is within the North Westgate development zone.
As a result, any extension "would need to be considered within this wider city development project and any potential land requirements".
It is hoped that the land required for the North Westgate development will be identified over the next year, but a commitment would have to be held off until these details could be determined.
The land is also designated Community Asset related land - meaning it is to be used for the well-being or social interest of the local community - and so permission would need to be obtained from Homes England before any change of use application could be made.
Cracknell said: "Homes England can require 36% of the land value in return depending on the new use required.
"There is an established process for release and this can take some time."
If approved, prior planning approval would be needed before the extension to the car park could go ahead.
Further consideration to extending Russell Street car park could be given from around July 2022.