Councillor Shaun Davies, Telford & Wrekin Council's leader, is calling for business owners to offer services and materials to fix up the buildings, which are within the hospital grounds.
The properties could house up to 12 people, more than enough to house the doctors needed to keep the A&E open.
Councillor Davies's call comes after it was announced Princess Royal Hospital’s A&E department would temporarily shut overnight to combat staff shortages.
But the Shrewsbury and Telford Hospital Trust said that if seven extra middle grade doctors and 15 A&E nurses could be found, it could remain open.
"Many people have been asking what they can do to support the hospital in the recruitment of doctors," Councillor Davies said.
"One of the things we've identified as a council is a pressing need for accommodation for junior and middle grade doctors.
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"Working with the Trust we have identified three houses that the Trust owns within the Princess Royal Hospital to house our junior doctors and our middle-grade doctors.
"Doing a deal with the Trust, they have said that if Telford & Wrekin Council and our community can refurbish those houses, they can then make them available for free for our junior doctors.
"That means that we will be the only hospital trust in England to provide free accommodation to those junior doctors we so desperately need at our hospital."
Councillor Davies said it was a "big ask", but that the effort could ensure the A&E stays open.
"I need your support," he said. "If you're a local business that can help us fit a kitchen, fit a bathroom, paint, decorate or provide materials, email today at NHS4All@telford.gov.uk
"Let's do all we can to secure those doctors we need to avoid an overnight closure at our A&E here at Telford and Wrekin."
The appeal has been welcomed by Jenni Rowlands, consultant cardiologist and director for undergraduate education at SaTH, who said: "It’s great to work with Telford & Wrekin Council to try to provide better services for our junior doctors who are our consultants of the future.”
Their comments come as a council-backed petition to the Government - at petition.parliament.uk/petitions/229602 - reaches nearly 21,000 signatures.
The strong response to the petition means the Government needs to issue a statement. It has been more than a week since the government passed 10,000 signatures – the number needed for an official response.
Telford & Wrekin Council are also organising a march through Wellington in opposition to the closure.
The protest will be held on November 4 over concerns that the department is facing temporary night closures and may be relocated under the Future Fit programme.
It is being organised by the campaign group NHS4All and Telford & Wrekin Council.