Learning Link Multi-Academy, which runs the sites in Dudley, has suffered a “serious breakdown” over how it is run and governed, a report said.
The Office of the Regional Schools Commissioner, in a termination warning notice, also raised concerns over the use of public money which is not being used in a “proper way”.
The academy trust runs Dudley Wood Primary School, Kates Hill Community Primary School, Netherbrook Primary School and Sledmere Primary School in the Dudley borough.
A report by Andrew Warren, schools commissioner for the West Midlands, said there had been a “vote of no confidence” in the trustees and acting CEO from the Netherbrook school.
And another letter has been submitted from members of the trust who have “no confidence” in regards to the “strategic direction” of the organisation.
Mr Warren said there had been a “collapse” in the senior leadership team – with no permanent CEO in place, along with the resignation of the chair of trustees.
It comes as the trust is “rebuilding” on a deficit at the end of 2018-2019, with the academy’s outstanding financial statements for the period not yet being submitted.
Financial accounts and a management letter have not been sent across – and no minutes from any trustee or committee meetings have been submitted to the Education and Skills Funding Agency (ESFA).
Governance of the trust remains “unclear” throughout, with information recorded on Get Information About Schools (GIAS) and Companies House not being consistent, the notice added.
Mr Warren, in the report, said: “I cannot have confidence that trustees and trust leaders are operating in accordance with the Academies Handbook, the Governance Handbook and Funding Agreement or that the trust is able to adequately address the significant challenges it faces.”
A spokesman for the Department for Education added: “We have issued a termination warning notice to Linked Learning Multi Academy Trust due to ongoing concerns about the governance and oversight of financial management by the board.
"We will continue to work with the trust as we consider next steps.”
Linked Learning Multi-Academy has been contacted for comment.
The full report can be read here.