"The president has not met with Mr Nxasana and has not asked him to resign," spokesman Mac Maharaj said.
Earlier National Prosecuting Authority spokesman Nathi Ncube said the article was a lie.
"The story is a pure fabrication by information peddlers with a very active imagination," Ncube told a Sapa reporter via sms.
Sources close to the NPA and the presidency reportedly told the newspaper that Zuma met Nxasana recently to discuss Nxasana's future.
It was at that meeting that Zuma reportedly asked Nxasana to resign or face being fired.
Nxasana then reportedly pleaded with Zuma to reconsider his position.
Nxasana told the paper the meeting did not take place.
"It never happened. He never asked me to resign. That I can assure you. We are communicating with the president. He is still applying his mind. I am sure once he has applied his mind it will be communicated to the media and the public," Nxasana was quoted as saying.
Reports have surfaced over Nxasana's background with claims that he was charged with murder in 1985 and acquitted on grounds of self-defence.