Peverley, 30, has two-years left on his current contract that pays him $3.375 million per year, though his cap hit is $3.25 million.
He has some say in where he could end up, if traded, but a deal is not yet imminent.
The Bruins have roughly $6 million in available salary cap space heading into next season and are trying to sign right wing Nathan Horton to a multi-year extension.
Horton is scheduled to become an unrestricted free agent July 5.
Boston GM Peter Chiarelli is also in negotiations to sign center Patrice Bergeron and goalie Tuukka Rask to contract extensions, and talks between the Bruins and Bergeron and Rask's agents are expected to continue over the weekend.
Bergeron has one-year left on his deal, but Rask can become a restricted free agent next week.