The decision by the former Australian captain follows Hansie Cronje's recent refusal, after it was initially reported he would coach Glamorgan.
The South African captain decided against the role because of his continuing commitment to international cricket, and now Chappell, South Australia's manager, has told Glamorgan he cannot combine the move with coaching his Australian Interstate Championship side.
Chappell said: "I've told them that I won't be coming, thanked them very much, but I just didn't feel that I could do justice to both jobs."
Navjot Singh Sidhu, the Indian opener, announced his retirement from the domestic and international game yesterday. Sidhu, who played his last Test in New Zealand in January, played in 51 Tests from 1983, scoring 3,202 runs at an average of 42.13 with nine centuries and 15 50s. His highest score was 201 against West Indies in Port-of-Spain in 1997.
Sidhu said he planned to enter politics and was "waiting for an offer".