The club has started to listen to teams looking to acquire the star forward, reports TSN's Pierre LeBrun, who adds that while it doesn't mean a trade is certain, Devils general manager Ray Shero is now in "listening mode."
Shero met face-to-face with Hall's agent Darren Ferris earlier this month.
Hall, a pending unrestricted free agent, is in the final season of the seven-year, $42-million contract he inked with the Edmonton Oilers in 2012.
Shero said in March there was "zero chance" he was going to trade the 2017-18 Hart Trophy winner at the 2018-19 trade deadline.
However, after a busy offseason that included the additions of P.K. Subban, Nikita Gusev, and first overall pick Jack Hughes, New Jersey enters Saturday's action with the second-worst record in the Eastern Conference.