Parise, a restricted free agent, was limited to just 13 games and three goals last season due to a knee injury that required surgery. In the five seasons prior, Parise led the team in scoring twice and missed a total of three games.
The Devils and Parise had been scheduled to have an arbitration hearing on August 3.
"I think, by avoiding arbitration, we can come out with something both parties agree with just four days before the arbitration hearing, it just sets the platform where both parties are going in the same direction," Devils general manager Lou Lamoriello said.
The two sides will continue to work on a long-term deal.
(Reporting by Mike Mouat in Windsor, Ontario. Editing by Ian Ransom)