The court will hear arguments Monday over a judge's denial of an injunction that would have stopped betting from beginning next month.
Attorneys for Delaware say the leagues have not met the requirements for an injunction. A trial on whether the betting would violate federal law or the state constitution is to begin in December.
Delaware is exempt from a federal ban on sports betting because it ran a sports lottery in 1976. But the leagues argue that the exemption doesn't allow Delaware to offer bets on single games or on sports other than professional football.