"We have started today advertising for a replacement for Tom Moody," Sri Lanka Cricket (SLC) spokesman Samantha Algama told reporters. He said notices would appear on SLC website.
"The short-listing of candidates will happen by the end of this month."
Moody, named coach in 2005, announced earlier this month that the ongoing three-match one-day series against Pakistan in Abu Dhabi would be his last assignment.
Sri Lanka Cricket chief Jayantha Dharmadasa and captain Mahela Jayawardene had wanted the former Australian all-rounder, who will take over at Western Australia next season, to continue.
Algama said SLC would appoint an interim coach for next month's home series against Bangladesh.
The name of former New Zealand captain and India coach John Wright has figured in speculation about Moody's possible successor.
Sri Lanka finished runners-up to Australia in the World Cup in the Caribbean last month.