However, the unit said on Thursday that it was intensifying its investigations into the matter, adding that it would only bring cases to court once the investigations had been finalised.
The Hawks would then, through the National Prosecuting Authority, implement the extradition treaty.
This comes after Parliament late last year approved the Extradition and Mutual Legal Assistance Treaty with the United Arab Emirates.
The Guptas are believed to be in Dubai after they left the country early last year. This was before the Hawks and other law enforcement agencies raided their property in Johannesburg.
Hawks spokesperson Brigadier Hangwani Mulaudzi said they would work to conclude the investigations before the extradition could happen.
“When you take a case to court you must have everything,” said Mulaudzi, adding that the matter was even discussed in Parliament.
He said they did not want to end up with a situation where they did not cover all the aspects of the cases.
“The rule of speciality, in terms of international law, says you cannot extradite any person to investigate. You extradite to prosecute,” said Mulaudzi.
“It means your investigation must be complete and there must be no additional charges when you bring those people to court,” he said.
The Zondo Commission of Inquiry into state capture has heard evidence implicating the Guptas in state capture.
Former cabinet minister Ngoako Ramatlhodi also dropped a number of bombshells in his evidence against the family and former president Jacob Zuma.
He said the family appeared to have a stranglehold on Zuma.
Zuma has denied any wrongdoing, but admitted the Guptas were his friends.
Deputy Chief Justice Raymond Zondo has called for more cabinet and former cabinet ministers to come forward and give evidence.
Parliament has also submitted its report to the Zondo Commission into the inquiry into Eskom where several individuals were implicated.
The national legislature has asked former ministers Malusi Gigaba and Lynne Brown to go to the commission.
The two ministers were in charge of the Department of Public Enterprises when state capture allegedly happened.
Both ministers have consistently denied being involved in any wrongdoing.
During the inquiry, Gigaba and Brown were grilled by MPs in 2017.
Zondo had asked for an extension of two years from President Cyril Ramaphosa to complete his work.
The Hawks said their head had pushed for the unit to finalise the investigations.