The NHL club announced that 25-year-old Geoffrion was considering retirement because of the lingering effects of a skull fracture and concussion suffered during an American Hockey League game in November.
A team statement said that "in light of his health condition, which has shown no significant improvement since he underwent surgery last November 10, he felt it was his responsibility to inform the Canadiens' management that he was considering retiring from professional hockey."
Geoffrion is expected to decide in the next few weeks whether to make it official.
The six-foot-one centre was skating for the Hamilton Bulldogs when he suffered a depressed skull fracture from a hit by defenceman Jean-Philippe Cote of the Syracuse Crunch during a Nov. 9 American Hockey League game at the Bell Centre.
The Plantation, Fla., native underwent surgery a day later to repair damage that his father Dan Geoffrion, who also played briefly for the Canadiens, said could have been life-threatening or caused brain damage.
Geoffrion won the Hobey Baker Memorial Award in 2010 as the top player in U.S. university hockey with the Wisconsin Badgers. He was selected in the second round of the 2006 NHL draft by Nashville.
He has eight goals and five assists in 55 career NHL games.