The young forward ended the season on a devastating note, after he received a five-minute boarding major for a hit on Los Angeles defenseman Rob Scuderi that preceded three power-play goals for the Kings and a 3-0 hole for the Devils, who went on to lose the Stanley Cup in six games.
In 32 regular-season games with the Devils, Bernier collected one goal and five assists for six points.
As for the rest of the fourth line, forwards Ryan Carter and Stephen Gionta are also potential unrestricted free agents, but contract talks do not seem to have progressed as much as they have with Bernier.
Gionta, who signed a two-way deal with an NHL cap hit of $512,500 two summers ago, had a strong post-season while centering the Devils' fourth line. He might have more options if he were to hit the market on Sunday.
Carter, who has expressed the desire to stick with the Devils, is hoping that there will be a breakthrough in negotiations before he becomes an unrestricted free agent on July 1.