Oral arguments are set for Monday.
The Hollywood superstar paid Peggy Detmers $300,000 to make the sculpture in the 1990s for a resort he planned in South Dakota's Black Hills. The resort was never built but he instead placed the sculpture at his Tatanka attraction near Deadwood.
A judge ruled last summer that this alternative placement did not constitute a breach of contract.
Detmers said she gave Costner a price break because she anticipated selling more artwork at the resort.
Costner filmed much of his Academy-Award-winning movie "Dances with Wolves" in South Dakota.