BP is seeking restitution for some claims paid out to businesses as part of the Deepwater Horizon claims program.
According to the AP, BP is asking the 5th U.S. Circuit Court of Appeals in New Orleans to grant restitution plus interest on some funds paid out to businesses prior to a October 2013 revision to the claims program.
The company won the revision after a federal court found the administrator for the settlement claims was not correctly matching the revenues 0f businesses filing claims to their expenses.
The exact amount that the company is seeking has not been disclosed yet.
A three judge panel will hear arguments on Thursday but a ruling is not expected immediately, the AP added.
In May, the 5th U.S. Circuit Court of Appeals ruled that BP can challenged some of the claims because it never directly waived its right to appeal when it inked a settlement agreement in 2012.
The company has paid about $5.13 billion in claims to 63,597 claimants for damages tied to the Deepwater Horizon spill.
BP reached an agreement with Louisiana, Florida, Mississippi, Texas and Alabama in July to pay a $18.7 billion to resolve the years long Deepwater Horizon case.
The agreement will cover claims from the five Gulf states as well as 400 local government entities, BP said.
The company was facing up to $13.7 billion in Clean Water Act penalties tied to the 2010 spill that killed 11 people.