The trade union federation's General Secretary Bheki Ntshalintshali says the decision was made during a special central committee, which analysed the events at its main May Day rally in Mangaung.
Two sources said that ANC party leaders would discuss the removal of Mr Zuma, sending the rand up 1.5 per cent against the dollar.
The hostility shown towards the president came after a request by three Cosatu affiliates that President Zuma be barred from addressing the rally.
"Cosatu's voice in the tripartite alliance is still important because of the political muscle they still have as a functioning organisation", Bezuidenhout said.More news: Mulvaney defends Trump budget's social safety net cuts
Earlier this month President Zuma was booed at a Cosatu May Day rally in Bloemfontein forcing him to cut short his speech.
Meanwhile, central to yesterday's media briefing regarding resolutions taken by Cosatu was the barring of Zuma from addressing Cosatu members from its events.
This according to labour expert Professor Andries Bezuidenhout, who said the strong anti-Zuma sentiment expressed by the SACP and Cosatu especially, is a symbolic issue which will have long term ramifications for Zuma's ANC.
There were also questions raised at the press conference about why Cosatu president, Sidumo Dlamini attended Zuma's birthday celebration in April.More news: Trump greeted with selfies and politics on arrival in Israel
"This shall be communicated to the ANC (African National Congress), including engaging on its implications for our alliance", the trade federation said.
On whether Cosatu may have violated long-standing tradition in the alliance of internal communication mechanisms before alliance decisions are communicated to the public, Pamla dismissed that.
The federation also appeared to blame Zuma's lack of leadership on the decision by General Motors (GM) to disinvest from South Africa.More news: Zidane Comments On UCL Final Battle With Juve