Jay Grossman, the agent for Kovalchuk, has said his client is open to returning to the NHL. Kovalchuk is on the NHL's voluntary retirement list, meaning he could only sign with the Devils, but can't sign until July 1.
"Ilya asked me to make his intention to explore the options to return to the NHL known to Ray Shero, which has been done," Grossman said in an e-mail to The Record of Bergen County, New Jersey.
Shero said he's keeping all options open regarding Kovalchuk's future.
According to the collective bargaining agreement, a player who returns to the NHL from retirement must get approval to do so from all 30 of the league's owners.
Kovalchuk, now 34, could join another team only through a sign-and-trade deal.
He retired in July 2013 -- just three years into his 15-year, $100 million contract with the Devils -- and signed with St. Petersburg of the Kontinental Hockey League.
It is not the first time that speculation has been raised about Kovalchuk's possible return to the NHL. In 2016, NHL deputy commissioner Bill Daly admitted there were "a lot of different rules that apply to his situation" and wouldn't give a direct answer when asked if Kovalchuk would have to sit out a year prior to returning.
Kovalchuk scored 417 goals and registered 816 points in 816 career games with the Devils and Atlanta Thrashers. He was the first Russian player selected with the No. 1 overall pick when he was taken by Atlanta in 2001. He was acquired by the Devils in February 2010, then signed his revised massive contract seven months later.
In 245 career KHL games, Kovalchuk has 107 goals -- including 32 for SKA St. Petersburg last season -- and 157 assists.
Kovalchuk has represented Russia at four Winter Olympic Games, nine world championships, one world junior championship and the 2004 World Cup.
The Associated Press contributed to this report.