Bloomberg has reported that the firm will make its case at a hearing today before US District Judge Stephen Larson in California.
The company will have to counter MGA's argument that a jury found only the first generation of dolls, which are no longer manufactured, infringed copyright.
Mattel was recently awarded $100 million in damages, equivalent to five per cent of the $2 billion it originally sought.
MGA says in court papers that the jury's copyright verdict "found no infringement beyond the first generation'' dolls and contends the jury also said Mattel shouldn't get anything from future Bratz profits.
MGA had $777.9 million in Bratz profits through June of this year on sales of $3.1 billion, according to a Mattel expert's testimony. MGA's expert said it was no more than $405.4 million.
Mattel says all Bratz models infringe by using the original head and face from drawings found to belong to Mattel. Future damages weren't sought in the earlier phases of the trial.
Copyright owners denied an injunction have to keep suing for infringement, Mattel said in its argument for a ban. In September, MGA's majority owner, Isaac Larian, rejected sharing Bratz revenue with Mattel as a way to settle the dispute.
"I have always said I want to settle for the sake of MGA employees and compete in the market place,'' Larian said in an emailed comment.
Mattel spokeswoman Jules Andres said the company "always has been open to good-faith settlement discussions.''