Highlanders chief executive Roger Clark confirmed Brown was not applying for the job.
"We would like to make a shortlist of candidates by the end of May and then by June hope to make an appointment."
Clark said former Australian and Crusaders coach Robbie Deans had also ruled himself out of the job.
Whoever is appointed will have to work with the other assistant coaches and will not be able to bring in his own staff.
"We have worked really, really hard to build a really high performing coaching and management team at the Highlanders and we are there now," Clark said. "It is important that the coach that we get is excited to be working with that high performing team and has that ability to take it to the next level."
Candidates
Scott McLeod
Experience: Chiefs, Waikato and Highlanders assistant
Chances: Seen somewhat as a backroom boy but a wise head.
Robbie Deans
Experience: Crusaders, Australia, Panasonic
Chances: Impressive resume and has done the job at this level with success. Is said to not want the job but don't count him out.
Rob Penney
Experience: Canterbury and Munster, coached in Japan.
Chances: Has the runs on the board but been overlooked before and is unlikely to get a chance again.
Tony Brown
Experience: Otago, coached in Japan, Highlanders assistant.
Chances: Would be favourite if he said he was keen but has ruled himself out and it will take a lot to change his mind.
Mark Anscombe
Experience: Auckland, Ulster coach.
Chances: Been in and around the scene for a good few years. Burned his bridges in Ireland.
Craig Philpott
Experience: Hawke's Bay, NZ under-20 assistant.
Chances: Well-regarded in higher circles and has done some good work with Hawke's Bay but has yet to taste coaching at a higher level.
Scott Robertson
Experience: Canterbury, NZ under-20.
Chances: Successful with Canterbury and NZ Colts but bound to be with the Crusaders next year.
Ewen McKenzie
Experience: Waratahs, Stade Francais, Wallabies.
Chances: Faded from the limelight but can coach.