West Midlands Ambulance Service has said moving its hub away from the Meole Brace area, where thousands of children attend local schools, is something it is working on.
But now Radbrook councillor Julia Evans has submitted a motion calling on Shropshire Council to work towards a solution as quickly as possible.
Several schoolchildren have been hit by cars in the area. Two mums launched a campaign group after one boy was hit by a car and another was involved in a frightening near miss.
Although the ambulance service has no recorded incidents of its vehicles being involved in a collision with a pedestrian in three years, parents are concerned about the traffic chaos caused by cars having to mount pavements to let paramedics drive through on blue lights and sirens.
More recently, a woman suffered a head injury after being hit by a youngster on a bike in Longden Road last week, and in October a man had to be cut free after a crash in Bank Farm Road.
In her motion, Councillor Evans calls on the council to urge portfolio holders to work towards a new ambulance hub site as quickly as possible, in order to facilitate much-needed road safety improvements in residential areas, investigate offering alternatives within the councils assets, in particular at Weeping Cross, and assist a teaching programme between schools and the ambulance service.
She also calls on the authority to assist WMAS with public information on how to drive and pull over when blue lights are seen and negotiate with them about incorporating a local Shropshire Ambulance Control within the new hub
At a Radbrook Road Safety Group meeting on November 25, a WMAS boss said that moving the hub was the organisation's "number one" estates priority.
Craig Cooke, the WMAS operational support services director, said: "The project is my next priority, my number one priority. There is no estates priority in front of this one. It has a lease life. We are serious about replacing this one."
Mr Cooke revealed that the hub is busier than it would normally be because of increasing pressures on the service.
"Every crew that books on has an emergency waiting for them," he said.
If pressures weren't so acute, ambulances would be out and about in the community instead. Chiefs hope that a bigger hub would be better for the Shrewsbury area where a rising population is increasing demands.
Councillor Evans' motion will be discussed at a full council meeting on Thursday this week. To view the meeting, which starts at 10am, visit bit.ly/3FhuoiU and click on the agenda front sheet to access the video link.