Coetzee is set to face a performance appraisal by a sub-committee of SA Rugby and will know in a week's time whether or not he will remain in the top job.
A stumbling block to Coetzee's removal will be the required £740,000 to pay off the remaining two years of his contract. With the South African rugby union in the red to the tune of around £1m, paying off Coetzee and also buying out the two-year contract Rennie has with Glasgow, figures for which have not been disclosed, could be out with their range financially regardless how much they rate the New Zealander.
Rennie, who has signed a two year deal with a one year option at Glasgow, has made clear that he had always planned to wait till after the 2019 Rugby World Cup to go into international coaching.
"There'll be a lot of international jobs come up after 2019 but ultimately the thinking is it will give me a couple of years at Glasgow and then give me a chance to see how things have gone," he said before he signed his deal with the Warriors.
A Glasgow Warriors spokesman said the club had no comment on the matter.