Moody will leave by the end of this month or before the T20 World Cup starts in Australia next month, another source said.
Former Sri Lanka head coach Moody was appointed director of cricket in February last year to help prepare the team for the T20 World Cup and the 50-over version in India in 2023.
There was no immediate comment from the Australian, who last month said that he was taking a similar director of cricket post at Desert Vipers in the newly formed UAE-based International League T20.
Under Moody, Sri Lanka emerged earlier this month as surprise winners of the Asia Cup, seen as a tune-up for the World Cup.
As director of cricket Moody drew up a performance-based pay structure which was resisted by the national squad.
But they were eventually forced to cave in following threats that they would be dropped unless they agreed.
Sri Lanka has faced acute shortages of food, fuel and medicines since late last year, but Sri Lanka Cricket remains flush with cash, according to board officials.
Last week it donated half a million dollars to a cancer hospital which is desperately in need of life-saving medicines and medical equipment.