The petition is being filed after an appeals court upheld part of a ruling by a California jury that found patent infringement by Samsung, ordering the company to pay $930 million in damages to its American rival.
The petition "will present at least two substantial questions concerning design-patent liability and damages," and be filed by November, the court documents filed Wednesday said.
Most petitions to the Supreme Court are not taken up by the body.
Samsung recently won a victory after a recalculation was ordered for a portion of the damages, but the company's counsel asked those proceedings to be halted pending the Supreme Court petition.
The recalculation could affect as much as $382 million of the award to Apple, which was on grounds the South Korean electronics giant hurt Apple's image by copying design features of the iPhone.
Many tech companies are involved in patent disputes around the world, but the Apple-Samsung case has drawn unique attention as they are both leaders in the smartphone and computer market.