The Hawks will have a new head by the start of June, Police Minister Bheki Cele told the Portfolio Committee on Police on Tuesday.
Cele said candidates were shortlisted last week Wednesday, but that there had been a problem with the advertisement of the post.
"The ad put us a little bit on the back foot," he said.
It was not immediately clear what the problem with the advertisement was, but he said the process had been started anew.
He also said the department wanted the new head of the Hawks to be announced at the beginning of May, but that this would now happen a month later.
Lieutenant General Yolisa Matakata is currently acting head of the Hawks, after her predecessor Lieutenant General Berning Ntlemeza's appointment was set aside by the North Gauteng High Court in March last year.
Much of the police's problems were laid at the door of the service's top brass by civil society organisations that briefed the committee earlier on Tuesday.
Instability contributing to corruption
Gareth Newham of the Institute for Security Studies said: "The system for identifying police officers who shouldn't be in the system isn't working."
David Lewis of Corruption Watch said the "chronic instability in police leadership positions" contributed to corruption.
He said Corruption Watch would launch a campaign to monitor the appointment of senior police leaders, and that the organisation was particularly interested in the appointment of the head of the Hawks.
"The criteria for becoming a police commissioner is far less onerous than for becoming a police officer," he said.
He said there were instances where the police seemed loathe to act on strong prima facie evidence of grand corruption, as in the case of Sassa/Cash Paymaster Services and McKinsey/Eskom.
He also said the prima facie evidence in the South African Revenue Service's Jonas Makwakwa matter was "enormously powerful" and that the organisation was so confident about the evidence in the public domain that it had asked the National Prosecuting Authority for a certificate for a private prosecution.
66 000 officers due for promotion
Cele said: "I think that it should be natural that if you do crime, you do time.
"The question of people (police officers) not doing... what they are supposed to do, underperforming cannot be tolerated."
He said last week the police arrested 17 of their own for corruption.
"We need to clean the police."
He said the SAPS needed more money to fund the promotion of more police officers. According to Cele, there are 66 000 police officers overdue for promotion. He said if police officers were adequately compensated, they would have "no excuse for doing wrong things".
National Police Commissioner Khehla Sitole said: "We do have capable senior cops, but they need to be put together and share a common vision."
He said when constables look at the police's top echelons, they needed to see hope.
"They must want to become police commissioner."