The presidency is demanding $635 million from two of the Oil Majors, Agip, and Total for the undeclared crude oil shipment from Nigeria between the years 2011 and 2014.
The oil companies have been sued at a Federal High Court in Lagos, and hearing into the case will come up next week.
Total is being asked to pay$490.5 million, while Agip will pay $145.8 million.
The case might be extended to chevron and ExxonMobil.
The claim is being based on a forensic analysis which proves that the volume of oil declared by the oil companies as exported from Nigeria into the us, lower than the import recorded from the point of entry in the us.