Cabinet members will vote on proposals next week to allow 470 desk-based staff to work a 30 hour four-day week from January.
A report published ahead of the meeting said Covid-19 has made “people think differently about work-life priorities; nationally and locally it is harder than ever to recruit and retain staff”.
The Lib Dem-controlled council said it would save around £1m a year if it could fill the 23 vacant posts that it currently hires agency staff for.
Both the public and private sectors are facing a recruitment crisis, not least due to older members of the workforce reaching retirement age.
Official data revealed earlier this year that 300,000 people have left the workforce in the last 12 months.
Bridget Smith, Liberal Democrat leader of the council, said: “The trial would be all about seeing if a four-day week has the same positive impact on productivity, staff wellbeing and recruitment in local government, as seen elsewhere.
“As a council we are leading the way on this; it could be truly ground-breaking for local councils nationally.
“As we look for solutions to these issues, these proposals suggest a robust, evidence-based trial for three months.”
The council’s proposal follows private sector pilots under the 4 Day Week Campaign, and research suggests improvements in attracting and retaining talent, improved employee satisfaction, reduced staff sickness, cost savings and increased productivity.
The report said that recent anecdotal evidence from across the council suggests that some colleagues feel stressed and are struggling at work, which has been recognised as a sector wide issue.
Over the last five quarters, the council has only been able to fill 80% of vacant posts, and it is hoped the trial could entice more workers to the authority, the council said.
“If the trial were to prove successful and we moved to being a four-day week employer, people would immediately benefit from a better work-life balance, and our recruitment problems would likely be significantly reduced,” the report said.
Officers added that improved staff retention would help to retain experienced and knowledgeable staff and give a greater service to residents.
If the initial results are positive, the council said it would continue the pilot through April and May, while the full results are analysed and presented to the employment and staffing committee and cabinet.
The council said it has proposed that a further would be run for blue collar staff if the initial trial is successful.
Joe Ryle, director of the 4 Day Week Campaign, said: “This move could benefit thousands of workers, improve productivity, and help to tackle the job recruitment crisis in local government.
“We hope this trial, if approved, results in many more councils across the country embracing the four-day week.”