Giordano suffered a torn biceps last week and will be lost for the season.
The 31-year-old, who has played with the Flames his entire NHL career, has 11 goals and 37 assists in 61 games this. His 48 points are tied for first among all NHL defensemen.
With 70 points, the Flames sit tied with the Los Angeles Kings for the eighth and final Western Conference playoff spot, although the Kings own the tiebreaker between the two squads.
The NHL trade deadline is Monday at 3 p.m. eastern time.
- Will Green