BP announced last week it reached a definitive agreement for $7.8 billion, paid to the Plaintiffs' Steering Committee, to settle the bulk of the claims related to the Deepwater Horizon oil spill in the Gulf of Mexico.
U.S. District Court Judge Carl Barbier was quoted by The Daily Telegraph newspaper in London as saying he was "leaning in favor" of the settlement claims from the British oil company.
BP attorney Rick Godfrey said the courts were considering whether the settlement was "reasonably fair and adequate to justify sending out notices."
BP still faces fines from the U.S. government for violations of the Clean Water Act.
A former engineer with the company was accused this week of obstructing justice by destroying electronic documents that suggested the company was giving misleading information about the amount of oil spilling into the Gulf of Mexico following the 2010 accident.
The judge, sitting in New Orleans, said it would likely be November before he issues a final approval.