It comes after Dudley Council and Dudley Clinical Commissioning Group were told action was required over “significant weakness” in the area’s special educational needs and disabilities (SEND) practices late last year.
Inspectors asked for a written statement of action to be handed over after their visit.
And headteachers and governors said they have a "complete lack of trust and belief in the SEND system”, it was reported.
Figures sent out to schools last year say the service could overrun by £22m by March 2024.
Now in an annual report, the head of audit services at the authority highlighted this year's funding shortfall as one of their main concerns.
The issue is mentioned in a report going to the audit and standards committee tomorrow.
The report says: "Ofsted and the Care Quality Commission (CQC) conducted a joint inspection of the local area of Dudley to judge the effectiveness of the area in implementing the disability and special educational needs reforms as set out in the Children and Families Act 2014.
"The inspection identified some significant weaknesses and required a written statement of action to be submitted to Ofsted.
"The cost of special education needs and disability (SEND) services are met from the High Needs Block within the dedicated schools grant.
"It is understood there will be an ongoing underlying shortfall and a cumulative deficit of around £13m by the 31st March 2021."
Last year a consultation was carried out over plans to transfer £1m from the borough’s mainstream schools to children with disabilities for the next school year.
But nine out of 10 of the educational leaders asked said they were against the plans.
Dudley Council has been asked to comment.