The case centres on engineering firm KBR, which admitted bribing officials.
A lawyer for Mr Cheney said allegations he was involved in the scandal were "entirely baseless".
Mr Cheney was Halliburton's chief executive before becoming vice-president to George W Bush in 2001.
A spokesman for the anti-corruption agency, Femi Babafemi, said the charges were likely to be brought against Mr Cheney next week.
Mr Babafemi said the charges were "not unconnected to his role as the chief executive of Halliburton".
KBR last year pleaded guilty to paying $180m (£115m) in bribes to Nigerian officials prior to 2007, when it was a subsidiary of Halliburton. The firm agreed to pay $579m (£372m) in fines related to the case in the US.
But Nigeria, along with France and Switzerland, has conducted its own investigations into the case.
Mr Cheney's lawyer, Terence O'Donnell, said US investigators had "found no suggestion of any impropriety by Dick Cheney in his role of CEO of Halliburton".
"Any suggestion of misconduct on his part, made now, years later, is entirely baseless," Mr O'Donnell said.Office raid
The bribes concerned the construction of a liquefied natural gas (LNG) plant in southern Nigeria.
KBR and Halliburton have now split, and Halliburton says it is not connected with the case against KBR.
Halliburton denies involvement in the allegations.
It has complained that a raid on its office last week by Economic and Financial Crimes Commission officials was "an affront against justice".
Ten people were detained for questioning and later released.
A prosecutor quoted by the Agence France-Presse news agency said those charged would include former and current leaders of Halliburton and officials from firms in a consortium involved in the LNG plant.
Nigeria is a member of the oil cartel Opec and is one of the world's biggest oil exporters.
bbc.co.uk 2 Dec 2010
Nothing new here.
Corrupt business dealings and corporate crime a (illegal) 'normality' at the top end of business / politics.
If and when these deals come out the real repercussions are muffled by the politicians and people involved, and generally the punishment, is not served.
Politicians then hide the fact of the allegations, by drawing attention that the information obtained, if from leaked document is 'illegal'.