Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
"We don't want to review the Constitutional Court, we want to review its powers," Zuma told The Star newspaper during an interview.
"It is after experiencing that some of the decisions are not decisions that every other judge in the Constitutional Court agrees with."
This was reportedly part of a democratic process to counterbalance the powers of the three arms of the state. According to the newspaper, the issue was raised by a deputy minister and ANC leaders at the party's national executive committee meeting two weeks ago and was discussed by Cabinet ministers.
Zuma told the newspaper it was a "general societal issue" that was being raised.
He questioned the logic of having split judgments and said judges were being influenced by the media.
"How could you say that (the) judgment is absolutely correct when the judges themselves have different views about it?" Zuma asked.
He said if decisions by Parliament could be challenged, there was nothing wrong with questioning the judiciary.
Democratic Alliance MP Dene Smuts called on Zuma to clarify his remarks.
"President Zuma will find that he is on the path to a full-blown confrontation with the Constitutional Court if his remarks really mean what they seem to mean, because the court itself decides the constitutionality of constitutional amendments," Smuts said in a statement yesterday.
"It is apparent from the president's remarks that irritation with some of the court's judgments lies at the root of the desire for review."
Last year, Cabinet announced that a research institution would be appointed to "review" the decisions of the Constitutional Court to determine how, if at all, they had contributed to "transformation".
Zuma then questioned the decisions taken by the Constitutional Court, saying "as an elected branch of government, (they) should be allowed to do what they want to do".