The Habs are primarily in the market for a top-six goal-scorer, prompting speculation that they've asked the Anaheim Ducks about forward Bobby Ryan.
Several teams, however, are hot on Ryan's trail, including the Philadelphia Flyers, Carolina Hurricanes and Ottawa Senators.
Bergevin's Canadiens have also been linked to Chicago Blackhawks right wing Patrick Sharp, who has a modified no-movement clause and could likely have to approve any deal the Hawks attempt to complete.
Sharp is a fan favorite in Chicago, though, and a deal might only be consummated if the Blackhawks are successful in signing unrestricted free agent sniper Zach Parise.
Bergevin was the assistant general manager in Chicago last season, which has also fueled speculation.