The Kings had ruled themselves out Sunday after Kovalchuk rejected their contract offer, leaving the New Jersey Devils as the favorite.
Kovalchuk's agent, Jay Grossman, said in an e-mail to ESPN.com that he would not comment, but had announced Monday via Twitter that his player would decide that day which team he would sign with. However, the situation has continued to drag on.
And now the Kings are back in the picture, a source involved in the talks said Wednesday morning. SKA St. Petersburg of the KHL also has made a contract offer, a source said.
On Monday, the New York Post reported the Devils were on the verge of signing Kovalchuk to a six-year, $60 million deal, which has not come to fruition.
On Tuesday, when contacted by ESPN.com, Devils general manager Lou Lamoriello said, "Everything is status quo, that's all I'm going to say."
Pierre LeBrun covers the NHL for ESPN.com.