About 30 candidates had applied for the post.
Stephan Morse, chairman of the Vermont Education Board and head of the Secretary search committee, said that the process is a month ahead of schedule.
He said four candidates have been picked by the committee and interviewed.
The committee will recommend three names to Gov. Peter Shumlin.
Morse says the panel hopes to make a proposal to the full board on Nov. 13.
The committee was formed after a law was passed that gives the governor the authority to make that appointment. It also elevates the state's chief education official from a commissioner to a Cabinet-level secretary.