Speaking by phone to ESPN.com, Bernier said, "I spoke with Dean at the end of the season, and he told me he can keep me there but also feels he kind of owed me the chance to be somewhere else (as a starter). So I guess we'll know in the next few weeks."
The report did not reveal a timetable for a possible trade. Teams mentioned as landing spots were the Florida Panthers, Minnesota Wild, New York Islanders, Philadelphia Flyers and Toronto Maple Leafs.
"It's actually exciting," Bernier said. "But I really can't control anything. It's up to Dean. If there's the right trade for him, I'm sure he'll make the right call."
Bernier, 24, is behind Jonathan Quick, who last June signed a 10-year contract, on the Kings depth chart. Bernier played 14 games this season after appearing in 16 in 2011-12. In 62 games since making his NHL debut in 2007, he is 29-20-6 with a 2.36 goals-against average and a save percentage of .912.
"I'm still part of the L.A. Kings and it's been a great ride, but I feel really confident and I want to get to the next level to get a real chance to hopefully be a No. 1 somewhere," Bernier told the website. "I'm sure the Kings will make the right decision. If I'm staying there, I'm staying there. If not, I'm ready for the challenge."