Instead of taking action, said Durban political analyst Thabani Khumalo, the party would handle the issue the same way it did with damaging allegations against senior EFF members over the VBS Bank scandal.
As a result of the close interaction of Rupert and Shivambu, according to a book titled The Stellenbosch Mafia: Inside the Billionaires' Club, which was written by Pieter du Toit, Shivambu spent an afternoon in Stellenbosch discussing potential business plans with Rupert.
The book also alleges that Shivambu asked for assistance to build a hospital in Limpopo and afterwards allegedly accompanied the chief executive of Remgro (a company owned by Rupert), Jannie Durand, to the Remgro-owned Fleur du Cap wine estate.
In the same book, it is claimed that Shivambu gave Rupert an insight into the bruising ANC leadership battle ahead of the party’s 2017 conference and told him that Cyril Ramaphosa would win the contest.
Shivambu is alleged to have developed a close relationship with the man, so much so that he advised him to polish his image by doing an interview with Power FM.
However, Khumalo, with Xolani Dube of Xubera Institute for Research and Development, believes that until Shivambu challenges the book in court its contents will be seen as the "gospel truth".
“There are many campaigns to discredit one another and that makes it difficult to tell whether the claims in the book are true or not. The responsibility of those who are victims of these campaigns is to take them to court to be tested,” Khumalo said.
Dube said the ball was in Shivambu’s court to prove the publishers right or wrong.
He added that there were precedents in the country where books were pulled from shelves or had paragraphs withdrawn when implicated figures challenged publishers.
“If someone is challenging the publication of the book and not taking the author or the publishing house to court, this is a clear indication that there is something fishy.
"How much more if someone claims to be revolutionary, knowing that the image of his political organisation is being tainted,” Dube said.
Shivambu told Independent Media in a short message on Sunday that the EFF would issue a statement in due course.
The party in a statement released on Sunday night said it noted media reports regarding Shivambu and Rupert's alleged relationship.
It further said that while there had been an interaction between the duo, in the form of text messages, suggestions of a "cosy relationship" between the two were "misplaced and false".
"The publishing of the book and the interviews by Rupert confirms the desperation of the Stellenbosch Mafia to capture the EFF.
"The threats to the deputy president that came as a result of what he said in Parliament are typical of the capitalist criminals who always intimidate political leadership into submission.
"The EFF calls on EFF members and vigilant South Africans not to be diverted by the desperation of Stellenbosch Mafia, which is trying to divert attention from the fact that the public protector has made adverse findings against their blue-eyed boys Pravin Gordhan and Cyril Ramaphosa."