The 28-year-old has an annual salary cap hit of $6.68 million with two-years remaining on his current contract.
It's believed the Detroit Red Wings, St. Louis Blues, Edmonton Oilers, Carolina Hurricanes and Philadelphia Flyers have all inquired about his availability.
The Flames are looking for a top-six scorer, despite signing free agent right wing Jiri Hudler to a four-year contract, to be included in a package, should they decide to deal Bouwmeester.
The two-time All-Star picked up five goals and 24 assists for 29 points in all 82 games with the Flames this past season.
