The Bruins are up against the salary cap and are believed to be shopping the likes of Rich Peverley and Chris Kelly in an attempt to free up some space.
Several teams have called and inquired about center Tyler Seguin, but he's unlikely to be moved unless the team gets an offer that includes two top-six forwards as part of a larger package.
The Bruins are also close to signing center Patrice Bergeron and goalie Tuukka Rask to long-term contract extensions.
Bergeron, who has one-year left on his current contract, has expressed his desire to play in Boston for the rest of his career.
"It would mean a lot. That's the goal,” he told the Boston Herald. "Since the beginning, it's a team that believed in me when I was 18 and coming up. It's my home. I love the city, love the people and definitely love the organization. It would mean a lot to me."
The Bruins are looking to replace right wing Nathan Horton, who will not be re-signing with the club.
Chiarelli has already had a conversation with free agent Danny Briere and is expected to inquire about David Clarkson, and said he might "revisit" talks with Jaromir Jagr on a possible return.