Part of the reason the Bruins didn't come to an agreement with Kovalchuk, a 35-year-old forward, is they weren't willing to give him a three-year contract.
"I don't think the term would have been idealistic for us and how we were looking at it," Bruins general manager Don Sweeney said.
Forward Rick Nash, who finished last season with the Bruins and can become an unrestricted free agent July 1, is a possibility to return with Kovalchuk going to Los Angeles.
Nash had six points (three goals, three assists) in 11 regular-season games and five points (three goals, two assists) in 12 games in the Stanley Cup Playoffs with Boston after it acquired him in a trade with the New York Rangers on Feb. 25. He missed the last 12 games of the regular season with a concussion before returning for the Eastern Conference First Round against the Toronto Maple Leafs.
"We've had great communication with Rick and his representative," Sweeney said. "We'll continue to do that, and whenever Rick makes a decision for his own future, we'll probably be open to continuing those."
Nash can begin talking with other teams interested in signing him Sunday, when the NHL's free agent interview period opens.
"The time is in his court at this stage to initiate whatever talks he wants wherever he wants to go," Sweeney said. "I think he's strongly indicated that Boston is a place he would consider, as would we. We have some business to attend to. The timing of his decision may or may not line up. Obviously, we'll be in touch with his camp."