Morrow, 34, registered 12 goals and 13 assists for 25 points in 44 games with the Dallas Stars and Pittsburgh Penguins this past season. Fourteen of those points were tallied in 15 games with Pittsburgh.
Carbonneau revealed that there has "been movement in recent days," with respect to talk between Morrow's camp and the Canadiens, but also indicated that there are other teams "intersted in his services."
He also added that he felt the Canadiens "were surprised (Morrow) was open to the idea of playing in Montreal."
In 850 career NHL regular-season games with the Stars and Penguins, Morrow has accumulated 249 goals and 293 assists for 542 points, along with 1,222 penalty minutes.
He was originally drafted 25th overall by the Stars in the 1997 NHL Entry Draft, and was traded to Pittsburgh on March 24.