Hall started the 2012-13 season with the Lightning, totaling four points in 20 games. He was claimed by the Hurricanes on waivers March 16, and had no points and a minus-2 rating in six games.
Lightning GM Steve Yzerman commented that he viewed the trade of Bergeron as an opportunity to add to his stash of draft picks.
"Our plan is to place Hall on waivers, and if he clears we will send him to Syracuse," Yzerman said of the forward who began the season in Tampa Bay.
"Marc-Andre hasn't played a lot for us this year and he's hoping to play. He's worked hard and been patient. He's been a good soldier. Through the process he's been really good about it, so I'm happy he gets a chance to play and not only earn a job for this year bur for future years."
Looking forward, Yzerman did not say he expected anything major to happen before the Wednesday trade deadline.
"We'll be busy, talking to other clubs, but I don't know that we will actually do anything," Yzerman said.
Asked if he had a "lot of lines in the water," Yzerman said, "I wouldn't describe it as that."
NHL.com correspondent Lonnie Herman in Tampa contributed to this report.