Kovalchuk, a 35-year-old forward who played the past five seasons in the Kontinental Hockey League, reportedly cannot sign with an NHL team until July 1 but can agree to a contract before then.
He reportedly has met with the Los Angeles Kings and the San Jose Sharks. The Los Angeles Times reported that he met with Kings president Luc Robitaille and general manager Rob Blake on Friday, and TSN said he met with the Sharks on Monday.
Kovalchuk hasn't played in the NHL since the 2012-13 season, when he had 31 points (11 goals, 20 assists) in 37 games for the New Jersey Devils. Playing for St. Petersburg SKA, Kovalchuk led the KHL in scoring this season with 63 points (31 goals, 32 assists) in 53 games. He has 285 points (120 goals, 165 assists) in 262 games during the past five seasons in the KHL.
Sweeney said he's not worried about Kovalchuk getting reacclimated to the NHL after his time in Russia.
"I don't think it's a problem integrating into the NHL," Sweeney said. "How he fits onto your team, the dynamic there, where he plays, those are things that obviously are unknowns. You can project and predict, but until the coach gets him on the ice and puts him in places, you just never know. But as far as the NHL, no concern there."