It launched in 2017 as a partnership between Wolverhampton Council and the Department of Work and Pensions but could be forced to shut down next March due to a lack of funding.
The news comes just six months after the scheme was celebrating reaching the milestone of helping 4,000 people into work.
Wolverhampton Council chiefs say they are now looking for ways to keep the service running after it “exceeded its targets”, running.
Council spokesman Paul Brown said: “There is a strong commitment from the council to continue this work in securing good jobs for residents and supporting businesses to bring future growth in our city.
“We are working with colleagues at the West Midlands Combined Authority to lobby Government and secure sustainable funding for this incredibly successful scheme.”
A report highlighting the potential closure is set to be presented to the city council’s Audit and Risk Committee on Monday.
The report said: “Wolves at Work is a joint partnership between DWP and the council aimed at supporting 3,000 residents into sustained employment over three years.
“Continuation of funding past March 2020 is now being explored.
“Future funding is a risk for Wolves at Work. Efforts are continuing to seek external funding from a range of sources.”
The scheme was projected to help 3,000 residents find sustained employment in the city, but has so far helped 4,487 people.
And around 45 per cent – or roughly 2,019 people – have been aged 18 to 29.
Businesses have also committed to the scheme by pledging work experience places and to create apprenticeships in the city.
A total of 30 work coaches are also currently in place, helping people get into work.
It comes as the number claiming unemployment benefits, including Universal Credit, in the West Midlands rose by 2,460 to 132,840, or 3.6 per cent of the working population in the three months to July.
Wolverhampton’s claimant count increased by 40 to 9,650, or 5.9 per cent of the working population.