And under the scheme, the nearby Frankwell car park could have a second floor added.
Councillor Peter Nutting said that while the Raven Meadows Multi-Storey car park is demolished the flatted shopping centre site could be used for car parking while the redevelopment is underway.
The council has been defending its decision to spend £51 million on the town's three shopping centres which it bought last year, and Councillor Nutting said he was confident that a return would be seen in the future.
Councillor Nutting said: "It [the demolition] is still being planned how we are going to do it but the intention is to start with the shopping centre and then move across the site.
"We have had the conversation many times about the car park, the multi-storey car park and everybody accepts that it is not the ideal design for the world we live in now so eventually that's got to go. What we would like to be able to do is drop the shopping centre and flatten that and use that as temporary parking for when the multi-storey goes.
"We are also looking at whether it is possible to put an extra level of parking on Frankwell and that might be one of the options as well because we have got to make sure there is enough parking in the town for while we are doing all this work.
"We think it will probably start in 12 months time."
Councillor Nutting also explained the council's plans to spend £4 million in renovating the Charles Darwin Shopping Centre.
"Part of it is refurbing and extending the toilet block on the middle level and making it in to a really decent toilets because even I think that some of the toilets around Shrewsbury need a revamp and can do with being a lot better than they are at the moment.
"People seem reluctant to invest money in toilets and yet when you go visiting to other towns it's almost the one thing you remember. We believe we can make them much better in both the shopping centres and that's going to be the start of the work. It's also about brightening up the lower levels by changing the ceiling heights and doing engineering work to brighten the whole place up.
"One of the things I want us to investigate is, and it's early days yet, we own the general market as well, and we have got queues of people who want to go in there. I'm looking at whether there is any opportunity to move some of the people from the general market in to the shopping centres. So that might be a possibility, we have just got to be careful how we do that."
Councillor Nutting also revealed that two major retailers were set to move in to the shopping centres in the 'next couple of months' but was unable, due to contractual issues, to say who they were.