Mayor Sheryl Mai said: "That's still under discussion with the current CEO."
However, Mr Simpson's contract expires in March and the council resolved this week to advertise the position to ensure a smooth, efficient and correct process was followed, Ms Mai said, adding Mr Simpson was entitled to reapply for the role.
"In 2011, he (Mr Simpson) competed against 40 candidates from across the country and was selected for the role."
In September, the WDC revealed that its cost for responding to Mrs Walters-Gleeson's claim to the ERA came to $184,609.12, including GST.
The cost of an earlier internal council review of her dismissal came to $9059, including GST.