The Hawks on Wednesday swooped on the Gupta family home in Saxonworld, where they reportedly arrested one of the brothers and an associate.
Enca is reporting that one Gupta brother and an associate have been arrested, but Hawks spokesperson Brigadier Hangwani Mulaudzi said it was "just speculation".
He said the Hawks had "concluded that operation" and were moving on to other addresses to continue their probe.
The Guptas have a close relationship with President Jacob Zuma and his family.
They are accused of using undue influence on government officials in charge of state-owned enterprises in order to score lucrative contracts.
In a separate interview, Mulaudzi said: "We are raiding that compound but we are not in a position to talk about it now. We'll give a comprehensive report later on because this thing of talking is going to compromise a lot," he said.
African News Agency (ANA) (and own reporting)