The local authority is at loggerheads with ENGIE, who maintain council buildings and provide cleaning and catering in around 80 schools across the district.
The dispute relates to the costs of transferring around 700 public sector workers to the French company in 2016, when a 10 year deal was signed.
Wakefield Council's annual statement of accounts said that it was seeking advice on the issue.
It is the latest development in a fractious relationship between the two parties.
In the statement of accounts document on its website, the council said it "is currently in dispute with ENGIE Services Ltd over the number and associated cost of staff transferred" when the contract began.
It added: "Reconciliation amounts due to or from ENGIE Services Ltd will be dependent on the interpretation of the contract.
"The council is currently seeking further advice on this matter."
A spokeswoman for ENGIE said the firm was unable to comment on the matter, as it was an "ongoing legal issue".
Last September, it was revealed that the company had been charged £100,000 by the council over a backlog of failures.
Councillors were told that ENGIE had not delivered on around 900 contractual obligations, and it was not presenting invoices accurately.
Officers said they could not "100 per cent" guarantee that the contract would last the course.
However, in its next update last March the council said that ENGIE's performance had "drastically improved", and that the two parties were meeting every fortnight to work through their issues.
Councillor Denise Jeffery, portfolio holder for regeneration and economic growth, said: "This is a contractual matter between the council and ENGIE which we are working on to reach a resolution.
"We continue to work in partnership with our ENGIE colleagues to deliver the property and facilities contract."
Local Democracy Reporting Service