The authority, which has a working balance of £22.6 million, could exhaust its financial safety net by 2021/2022.
But finance officials from Grant Thornton, which put together an audit report, believe the council's position could become "unsustainable" at an earlier date.
Now council bosses are set to look at ways to reduce the reliance on the General Fund reserves.
It comes after the authority underspent by £3.4m – despite having to use £4m from its cash pot.
The report, due before the audit and standards committee on Monday, says: "At the time of setting the 2019/20 budget, the council did not identify and agree a strategy to prevent its forecast general fund reducing to an unacceptably low level by the end of 2021/22.
“In addition there are significant risks to these forecasts that mean that the financial position may become unsustainable at an earlier date.
"The continued planned use of balances only buys the council time in which to develop a sustainable financial strategy.
"In our view it is vital that further income growth is achieved to close the financial gap and ensure that the finances of the council are sustainable in the medium term."
Councillor Steve Clark, cabinet member for finance and legal services, said: “In Dudley we continue to have one of the lowest council tax rates in the region, which means we bring in less money each year to spend on council services compared to some of our neighbouring and similar sized authorities.
“This has inevitably had an impact on our financial position and meant we have had to use our reserves.
"The auditors, in drawing their conclusion, have recognised that we have made better than expected progress to improve our financial resilience but acknowledged there is more to do to sustain our finances long term.
“We will continue to look at how we can work more efficiently across the council to reduce the reliance on the council’s reserves moving forward.”
It comes after councillors discussed raising council tax by an average of £46, or three per cent, last month.