Anwar unleashed a furore last month when he released the recording in which a well-connected lawyer appears to be telling a senior judge over the telephone that he would push his name forward for a senior appointment.
He said the whistleblowers, who witnessed the conversation taking place, will only come forward if the government can guarantee their safety.
"At the right time, these people will come out. Give them an undertaking today, and in a few days they will come out and Malaysians will know the truth. Their issue is personal safety," Anwar said.
"Attempts to incarcerate the whistleblowers will serve to further exacerbate the public's outrage and will certainly draw the condemnation of the international community that is monitoring developments in this case," he said.
Anwar was speaking to reporters after a two-hour meeting with the Anti-Corruption Agency (ACA) who quizzed him on the video recording.
The government has set up an independent three-man panel to investigate the authenticity of the recording amid calls by opposition, lawyers and rights groups for a royal commission of inquiry.
Anwar said the whistleblowers will reveal all the details if a royal commission were to be held.
He said the independent panel's probe would be a futile exercise as it does not have the power to compel witnesses to come forward.
The ex-deputy was heir apparent to former prime minister Mahathir Mohamad until his sacking in 1998, when he was hit with sodomy and corruption charges that landed him in jail for six years.
The sodomy conviction was later overturned but the corruption verdict stands, barring Anwar from standing for public office until April 2008.
He is adviser to Keadilan or People's Justice Party, which is formally led by his wife.