The trial heard allegations that sexual liaisons between teachers and pupils at Chetham's were not uncommon, and during the proceedings Brewer himself admitted an affair with a 17-year-old pupil which led to his resignation in the mid-1990s.
Chief Superintendent Russ Jackson said: "Following the conclusion of the trial last week there has been substantial press coverage and comment. Greater Manchester Police has since been provided with a list of potential victims from a newspaper.
"In addition to this, several people have also come forward directly to police. Reporting sexual abuse which occurred some time ago is an incredibly difficult thing to do, so we will be affording them, and anyone else who comes forward, all the appropriate time and support to discuss events in their own time.
"We will be working very closely with the school in the coming weeks and months but I must stress this investigation is at a very early stage. I would urge anyone who wishes to report abuse at the school to contact Greater Manchester Police on 101, or Crimestoppers, anonymously, on 0800 555 111.
"We have specially trained officers on hand to deal with any complaints sensitively and expeditiously and I would encourage any victim of sexual abuse regardless of when or where the offence occurred to call us."