The Blues have the fourth-worst record in the Western Conference and may be looking to move Kariya, Tkachuk, defenseman Carlo Colaiacovo or right wing Brad Boyes before the trade deadline.
Kariya has struggled this season, posting 12 goals and 17 assists with St. Louis. The 35-year-old former University of Maine star has recorded 975 career points in 15 NHL seasons.
The Bruins have been active on the trade market, acquiring defensemen Steve Kampfer and Cody Wild in separate trades on Tuesday. Chiarelli is reportedly looking to acquire an offensive-minded forward before the deadline.