Kovalev led the Canadiens in scoring with 65 points in 78 games despite being sent home for a few days during the season by General Manager Bob Gainey.
The season was a drop-off from Kovalev's resurgent 2007-08 output, when he had team-highs of 34 goals and 84 points, and led the Canadiens to the best record in the Eastern Conference.
But almost season-long discord and off-ice issues overtook the locker room, compounded by the spotlight of the 100th anniversary celebration that seemed to add unnecessary pressure.
Kovalev could be buoyed by Tuesday's acquisition of center Scott Gomez from the New York Rangers. Kovalev never jelled with captain Saku Koivu -- also an unrestricted free agent -- and Tomas Plekanec showed last season he wasn't ready for a top-line role.