It comes after a decision to expel a pupil who made threats with a knife was allegedly overturned.
GMB, which represents 30 support workers at Saltley School including caretakers and cleaners, said it would send the letter next week.
Teachers voted last week not to teach the unidentified pupil, who is currently not at the school.
"We're writing a letter of no confidence and teachers will be able to sign that before it's sent to the governing body," confirmed GMB spokeswoman Gill Whittaker.
Ms Whittaker said they wanted a new governing body if the pupil was not going to be expelled, one that was "representative of the whole school."
A handful of parents gathered outside the school earlier, to find out what action was going to be taken.
The council said teachers were "working normally" and the pupil in question "was not at the school at the moment".
Head teacher Balwant Bains has declined to comment on the issue.
He has previously said he has "total confidence in the safety of staff and pupils".
Teaching union the NASUWT has said it hopes to have further talks with the school.
Police said they took no further action after an incident on 22 May.
A union has announced it will be sending a letter of no confidence to a Birmingham school's governing body.