According to posts on Talk Radio 702 breakfast host John Robbie's Twitter profile, who interviewed Nyoka this morning, the CSA president said Majola lied to him about IPL staff bonuses.
Nyoka was speaking after reportedly being asked to step down from his post.
"Dr Nyoka says he was lied to over the payment of IPL bonuses to Cricket SA officials. Was told none were paid," tweeted Robbie.
"Dr Nyoka says Cricket SA will never be able to bury the truth," Robbie wrote on the social networking site.
Nyoka and Majola clashed last year following reports that the CEO and dozens of other CSA employees received bonuses for successfully hosting the ICC Champions Trophy and the IPL
Champions League in 2009.
Majola was cleared of any wrong-doing in an internal investigation.
"Cricket is not a secret society... not Stalin's Russia," Nyoka was reported as saying by 'Sports24'.
Also in the interview, Nyoka apologised to Gauteng Cricket Board (GCB) chairperson Barry Skjoldhammer over the way he treated Gauteng Cricket and the Wanderers.
In 2009, Nyoka said no international cricket matches would be played at the Wanderers until the GCB had apologised for allegations made against Majola that he mismanaged the IPL event.
Robbie said Nyoka made an "unconditional apology over the issue".
Nyoka in the interview said he himself had not been fired or resigned, but had received a letter calling him to a meeting to discuss his position.