The pick can become a fourth-rounder if the Sabres make the playoffs and Simmonds plays in 10 games, according to reports. New Jersey reportedly retains 50% of Simmonds' salary.
The Sabres are eight points out of the second wild card.
Simmonds, 31, was signed in July to be part of New Jersey's reboot. The Devils had surprisingly made the playoffs in 2017-18 but regressed to eighth place in the Metropolitan Division last season.
Simmonds was acquired at the trade deadline last season by the Nashville Predators, who were hoping that his toughness and net-front presence would help bolster their playoff chances. But he had only three points in 17 regular-season games and skated in only two playoff games as Nashville was eliminated in the first round.
He signed a one-year, $5 million deal with New Jersey in July.
Simmonds' best seasons came with Philadelphia, where he was a 30-goal scorer twice and a fan favorite for his physical style.