Samoa Rugby Union (SRU) chief executive Faleomavaega Vincent Fepuleai told Radio New Zealand that a full review of their World Cup campaign was currently being undertaken.
"Stephen has called it a day, I guess, and there will be opportunities there and I think we will go through the proper process in recruitment of a new head coach and so forth," he told the broadcaster.
"The position would be advertised internally and externally and we will secure the best person who we think will take us over the next four years to World Cup success."
An SRU spokesperson said Betham had signalled his intention to step down but would not confirm it until the conclusion of a post-World Cup review.
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Betham took the role in 2012 and guided Samoa to victory in the Pacific Nations Cup that year before leading them to a famous win over Wales at the Millennium Stadium on a season-ending tour.
The following year he took Samoa to a first win over Scotland and another over Italy before runner-up finishes at the 2014 and 2015 Pacific Cups.
(Reporting by Ian Ransom in Melbourne; Editing by Patrick Johnston)
