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READ: Ex-Bok skipper calls for Coetzee's head
Knives are out for Coetzee after the Springboks' record 38-3 defeat to Ireland in Dublin this past weekend.
It was Ireland's biggest ever win in 111 years over South Africa and leaves Coetzee with a paltry 41% win record in 22 Tests in charge of the national team.
A report in the Sunday Times over the weekend stated that the top brass at SA Rugby are losing patience with Coetzee and his remaining time as head coach "can be counted in weeksamp;sbquo; not monthsamp;".
But Du Plessis - who was fired as head coach after just eight Tests in charge of the Springboks in 1997 - told Netwerk24 that SA Rugby should not make hasty decisions regarding Coetzee's future.
"Is our rugby strategically positioned in such a way for the Boks to remain one of the big guns in world rugby?amp;" Du Plessis questioned.
"No one likes to see the Boks lose by 40 points and it's easy to criticise afterwards. But will things without doubt be better (if Coetzee is fired) or is the problem bigger than the head coach?amp;"
Du Plessis, who coached the Boks to a 2-1 series defeat against the British and Irish Lions in 1997, lost his job after winning just three of eight Tests - a 37.5% win-percentage.
The 57-year-old Du Plessis, who was known in his playing days as the 'Prince of Wings', played 12 Tests for the Springboks between 1982 and 1989.