He reportedly cannot sign a contract until July 1 but can agree to one before then.
The Los Angeles Times reported Saturday that Kovalchuk visited the Kings' practice facility and met with team president Luc Robitaille and general manager Rob Blake, among others.
Kovalchuk voluntarily retired from the NHL on July 11, 2013, with 12 years and $77 million remaining on a 15-year, $100 million contract he signed with New Jersey on Sept. 3, 2010. He signed a four-year contract with SKA St. Petersburg on July 15, 2013.
When Kovalchuk left the NHL, his contract was terminated and he was placed on the voluntary retirement list. That allowed the Devils to maintain his NHL rights until he turned 35. Prior to then, Kovalchuk would have needed approval from all 31 NHL teams if he wanted to sign with another team.
The Devils before this NHL season said no team made them a trade offer in an attempt to sign Kovalchuk, a two-time 52-goal scorer who had 816 points (417 goals, 399 assists) in 816 NHL games with the Devils and Atlanta Thrashers, who selected him with the first pick in the 2001 NHL Draft.