Manyi, a staunch supporter of Eskom boss Brian Molefe, said that Treasury was “duty-bound” to protect the public purse.
As finance ministers, the three should be held to account if it was found that there had been anything “untoward”.
The complaint centres on the multibillion-rand tender issued for the construction of two power stations, Medupi and Kusile in 2007.
Described by commentators as one of the “most expensive projects in the world”, Manyi said that Eskom paid double what it should have.
Spokesperson Oupa Segalwe said that the complaint would first be assessed to determine whether it had any merit.
This process usually takes five days, but could be longer.
It was reported last week that Manyi had laid a charge against the Public Protector, Thuli Madonsela, accusing her of bias and of focusing on ANC corruption. He said he wanted the police to investigate.