Devils general manager Lou Lamoriello told the Associated Press on Monday that he planned to buy out both players' contracts if they were not claimed.
White, 33, has one year and $3 million left on his contract. He had six assists in 69 games last season, and has appeared in 743 games over 11 seasons, all with the Devils.
Hunter, 31, was acquired from the New York Islanders last week in exchange for another veteran forward, Brian Rolston. He missed most of last season with a torn MCL.
Hunter had two years and $4 million left on his contract. He has played all nine of his NHL seasons on Long Island.
New Jersey's cap hit for buying out the pair is $1.67 million for next season.