Shortlisted candidates will be interviewed by a selection panel, which will make recommendations to Mr Brown on April 14.
The mayor will then present his appointments to the governing body of councillors for endorsement on April 17.
Mr Brown, 57, and Ms Chuang, 32, began their affair after meeting at a council function in May 2011.
Sordid details of the affair, including claims they were once caught having sex in the Ngati Whatua Room of the Auckland Town Hall by a security guard, were revealed by the right-wing Whaleoil blog two days after October's local body elections.
The affair with a woman 25 years his junior, a failure to declare hotel stays and censure by councillors have dogged Mr Brown, who has vowed to redeem matters at home and stay in office.
Former panel chairwoman Dr Camille Nakhid supports Ms Chuang's right to apply for a position on the panel.
"She should be allowed to apply just as any other applicant ..."