Chiarelli met with the Oilers organization Tuesday to discuss his candidacy for an upper management position, according to SportsNet.
It is unclear what position Chiarelli would take on with the Oilers. Craig MacTavish is the Oilers' current general manager, and Kevin Lowe is the president of hockey operations.
Edmonton fired head coach Dallas Eakins in December when the team was mired in a 1-15 stretch. Edmonton finished the 2014-15 season 24-44-14, the second-worst record in the Western Conference.
TSN were the first to report the news, as noted below.
The Bruins fired then-GM Chiarelli on April 15. He had spent nine seasons leading the team, winning a Stanley Cup with the club in 2011 and reaching the Stanley Cup finals in 2013.
The Bruins missed the playoffs in 2015 for the first time since 2007.
- Will Green