It comes as plans to create a new Shirehall in the centre look set to be abandoned, throwing its future into doubt.
David Sandbach, former chief executive of Telford's Princess Royal Hospital, said providing such services from the site would give better access to patients and help boost the local economy.
He said: "I have been campaigning for many years to move outpatients, physiotherapy and diagnostic services from Royal Shrewsbury Hospital to the town centre.
"These services are used by around 150,000 people plus chaperones each year.
"Many of these patients are from east Shrewsbury and have to catch two buses to get to RSH.
"I believe that it is much fairer to base these services in the town centre.
"The existing redundant space in the Pride Hill Centre could be easily refitted to accommodate this kind of activity."
He said people would be able to combine their healthcare appointment with going shopping and it has the opportunity to increase footfall, potentially benefitting local shops.
It comes as there are plans for a brand new health and wellbeing hub in Shrewsbury catering for a range of health services provided by the NHS, local council, and voluntary organisations under one roof.
A location for the facility has yet to be found.
Shropshire, Telford and Wrekin Clinical Commissioning Group is calling for people to share their views about the proposals by filling in a survey at surveymonkey.co.uk/r/ShrewsburyHealthandWellbeingHubListeningExercise before the end of Sunday.
Figures have shown a rise in the average number of GP patients at practices in Shropshire, Telford and Wrekin.
Meanwhile, a report on the future of the Pride Hill Centre is due to be discussed behind closed doors by Shropshire Council tomorrow.
The paper was due to be published this week before officers decided in a last-minute u-turn that it had to be kept secret on grounds that it contained sensitive financial information.
It contains details of why the council now plans to abandon proposals to turn the Pride Hill Centre into its new headquarters, and instead build a new office block in the Riverside area.
The council closed the shopping centre earlier this year after deciding it wanted to sell Shirehall and move to a new base in the shopping centre.
Tomorrow's meeting of the full council will be held at Theatre Severn, starting at 10am.
The report will be presented following a vote to exclude the press and public.