Rhule sent packing from Springbok squad
Daniel du Preez and Sibusiso Nkosi are the other two players released from the squad. The duo will return to Durban on Tuesday to join up with the Sharks, while Rhule will re-join the Cheetahs and is available for Pro14 selection.
Coetzee will announce his matchday 23 on Thursday in Bloemfontein.
A lot of criticism was levelled towards Rhule after his performance in the Boks' 0-57 defeat to the All Blacks in Albany. The wing missed a number of tackles out wide and proved to be a liability on defence.
"We forget how good Raymond Rhule was against Australia," Coetzee said earlier this week.
"I am not the kind of coach that will just look at one game, one poor performance then I chuck him away.
"He was outstanding against Australia. There are few things that the All Blacks targeted and we will work on that. We will get that right and get him [Rhule] better."
With Rhule and Nkosi gone, it opens the door for Western Province star Dillyn Leyds to come into the starting XV for Saturday's clash against the Wallabies in Boemfontein.
The Springboks finish their 2017 Rugby Championship campaign against the All Blacks in Cape Town on October 7.
By Warren Fortune, in Bloemfontein