A spokesperson for the fire service said: “We are aware of claims referencing our Chief Fire Officer and West Midlands Fire Service.
“Formal enquiries and processes, in line with our Fire Authority’s constitution, are now ongoing in relation to the matters raised. We will undertake this thoroughly and fairly.
“In the meantime, we will not be commenting further.”
Separately, Mr Brown is also involved in a court case, in which a man has been charged with harassment against him.
Benjamin Walker was due to appear at Birmingham Magistrates Court on Tuesday but the case was vacated, pending a pre-trial hearing due to take place in February.
The Fire Brigades Union said it was aware of the allegations made against Mr Brown.