The 26-year-old American posted career highs in goals (33) and points (84) with the Devils last season, when he made $2.204 million.
New Jersey has 48 hours to accept the arbitrator's ruling and sign Gomez or let him become an unrestricted free agent.
"He's been an integral part of our success, no question," Devils president and general manager Lou Lamoriello said Tuesday night. "He's an excellent hockey player, but we have a lot of excellent hockey players. So we'll do the best that we can."
The Devils may have trouble accommodating Gomez under the salary cap at $5 million. They signed Patrik Elias to a $42 million, seven-year contract and Colin White to an $18 million, six-year deal this offseason and are already near the $44 million cap.
Teams are allowed to go as much as 10 percent over the cap during the offseason, but they must get back to it by the opening day of the regular season on Oct. 4.
"When the first day of the season comes, we will be where we need to be," Lamoriello said.
The Devils were above the cap before the season opener last year before they traded left winger Jeff Friesen and his $2.28 million salary to Washington for a conditional draft pick.