The Hawks -- the police's elite high-priority crimes unit -- on Wednesday arrested three people as they raided the posh home of India-born Guptas, a controversial business family linked to Zuma, who resigned on Thursday.
Ajay Gupta the patriarch of the embattled Gupta family is "on the run" and surrounded by a team of heavily armed bodyguards, Times Live reported quoting police officials.
Hawks officials confirmed that Ajay Gupta was a fugitive from the law and that they had obtained a warrant for his arrest, the report said.
The warrant comes amid media reports indicating that Ajay Gupta's brother Atul was also being sought.
Their nephew Verun Gupta on Thursday appeared before the Bloemfontein Magistrate's Court on charges of corruption, fraud and theft, the report said.
The charges relate to the theft of 220-million rand (USD 19 million) from the Free State agricultural department.
Verun Gupta appeared alongside his co-accused and Gupta family lieutenants Ronica Ragovan Ashu Chawla Nazeem Howa Kamal Vasrum and Free State agricultural officials Peter Thebetha and Takisi Janki Masiteng and chief of staff of national mining department Sylvia Dlamini.
Howa Gupta Chawla Vasrum and Gupta were released on 200 000 rand bail each while Thebetha Masiteng and Dlamini were each released on 10 000 rand bail, the report said.
They will appear in court again on August 17.
Hawks spokesman Brigadier Hangwani Mulaudzi confirmed that they were searching for Ajay Gupta.
"He has surrounded himself with bodyguards. We spoke to his lawyers he was meant to be surrendered but never did.
"We have issued a warrant of arrest for him. Although those protecting him must know they are protecting a wanted suspect. They will be charged with aiding and abetting a suspect," the officer said, adding that they had flagged border posts and were hoping to close in on Ajay Gupta soon.
On Wednesday, the Hawks carried out raids at the home of the Gupta family in the plush suburb of Saxonwold in Johannesburg in connection with the Vrede farm investigation.
The Gupta family owns a range of business interests in South Africa, including computing, mining, air travel, energy, technology and media.
The three brothers, Atul, Rajesh and Ajay, moved to South Africa in 1993 from India, just as white-minority rule was ending.
They are known friends of 75-year-old President Zuma - and his son, daughter and one of the president's wives worked for the family's firms, media reports said.
The Gupta brothers have been accused of wielding enormous political influence in South Africa, with critics alleging that they have tried to "capture the state" to advance their own business interests.
The Vrede farm investigation relates to the Estina dairy farm near Vrede, in the Free State, a project which was originally meant to help poor black farmers but from which the Gupta family are alleged to have pocketed millions of dollars, the allegations they deny.
Zuma's links to the Guptas are one of the reasons he resigned before the 2019 general election. The Guptas and Zuma have denied all allegations of wrongdoing.