The suit was filed by a Jets season ticket holder who also is an attorney.
They'll argue the case before the 3rd Circuit in Philadelphia on Wednesday. It was dismissed by a federal judge in New Jersey last year.
The Patriots were caught taping signals by Jets coaches, a violation of league rules, during the opening game of the 2007 season at Giants Stadium, won by New England.
The NFL fined head coach Bill Belichick $500,000 and the team $250,000, and stripped New England of a first-round draft choice.