The South Korean firm wants the patent verdict overturned, or the sum reduced.
If Samsung does not get its way, it can still challenge the verdict in the US appellate court and the US Supreme Court, the BBC reports.
It alleges that Velvin Hogan 'deliberately concealed information' about a lawsuit he had been involved in against hard drive-maker Seagate nearly 20 years ago that resulted in him filing for bankruptcy.
According to the report, another Samsung strategy focuses on the two iPhone design patents it was found guilty of infringing.
Both describe the exterior look of the handset, and Samsung says they should have been treated as one invention, which would have meant a smaller damages award, the report said.
Meanwhile, Apple is hoping the judge will boost the size of the payment to 1.77 billion dollars, the report added. (ANI )