The 53-year-old was appointed as Heyneke Meyer’s successor on a four-year contract following the World Cup last year.
However, South Africa have lost eight of their Test matches in 2016, including Saturday’s 27-13 defeat at the hands of Wales in Cardiff.
The Springboks have won a total of four matches from their 12 internationals this season and Coetzee’s has come under growing pressure.
The former Stormers boss insists he is thinking about the sack and has urged the squad to find a better level of performance.
Coetzee said: "I don't fear anything, to be honest.
"Collectively, we've got to understand that it's not just one person that can take responsibility for that.
"If I'm solely held responsible for that, then I will walk away.
"We need to get the standards up. The Springbok stands for excellence. We need to make sure that whatever systems we put in place will give the players a platform to achieve excellence."