The position is set to become available from February when current incumbent Graham Ford's contract expires.
Ford has opted not to renew his deal with the Sri Lanka Cricket Board so the search for his successor has begun.
Only 11 applicants applied for the post initially, none of whom interested the board, who then turned to Rixon in a bid to tempt him away from Australia.
Rixon, who has previously coached New Zealand, was not impressed with the terms proposed to him and voiced his criticism of the board.
"Sri Lanka Cricket sent me a contract which was really embarrassing, I have to say, because it was so poor," the 59-year-old said.
"I'm the assistant coach of Australia, and I get more staying with the job than on the contract they sent through.
"It was really quite embarrassing for an international coach.
"I was looking forward to sitting down and talking to someone, but no one's really given me that respect I suppose, to be able to do that. And I said no, I'm not really interested."
Former Sri Lanka international Marvan Atapattu and Sussex coach Mark Davis have been named as the two men on the shortlist to replace Ford.