Kucherov, 23, led the Lightning last season with 66 points and was second with 30 goals. He played for Team Russia at the World Cup of Hockey 2016 despite not having a contract for this NHL season.
"[Kucherov] is a great player, exactly what we want as a player and a person," Yzerman recently told the newspaper. "I'm very hopeful we can get something figured out."
Kucherov is one of a number of high-profile restricted free agents negotiating his contract. Another, Buffalo Sabres defenseman Rasmus Ristolainen, is skating at training camp while talks continue.
Yzerman said with Kucherov back from the World Cup, he will step up his efforts to work out a contract.
"I think a lot of it is the system," Yzerman said. "With the restricted free agents, there's not really a hard deadline. Closest deadline you can have is probably the first day of training camp or first day of the regular season, because now both sides really [have] to make a decision. Is the player willing to hold out? Every year there's a half-dozen, and this year there seems to be a few more of the restricted free agents without [arbitration] rights not yet signed. And I would assume, history has shown, gradually over the next couple weeks they all eventually get signed."
