The Islanders, Lightning, San Jose Sharks, Dallas Stars, Boston Bruins and Toronto Maple Leafs made presentations to Tavares during the NHL interview period that began Sunday.
"It's not illegal tampering, it's a period to talk to free agents and I do personally like it," Yzerman said. "It gives everybody a chance to think it through. As opposed to July 1 when everyone ... the players, the agents and the teams are making decisions as quickly as possible under duress. ... So I think it's a better process."
Yzerman said Tavares is "one of the best players in the League" and the decision to pursue him or any free agent is to help make the Lightning a better team.
"We look at every opportunity that comes along, and in our opinion, does this make us a better team?" Yzerman said. "It's kind of as simple as that. Hopefully we're right more times than we're not."
The Lightning on Tuesday signed forward J.T. Miller to a five-year contract with an average annual value of $5.25 million and reportedly are trying to sign defenseman Ryan McDonagh to a long-term contract.
The Lightning also can sign forward Nikita Kucherov to a contract extension beginning July 1. He signed a three-year contract with an average annual value of $4.766 million as a restricted free agent during the 2016-17 season.
To make room under the NHL salary cap, the Lightning possibly could trade forwards Tyler Johnson and Alex Killorn. Johnson finished the first season of a seven-year contract that has an AAV of $5 million, and Killorn completed the second season of a seven-year contract that has an AAV of $4.45 million.
The Lightning season ended when they lost the Eastern Conference Final to the Washington Capitals. Tampa Bay was shut out in Games 6 and 7 did not score in the final 159:37 of the series.
The Islanders selected Tavares with the No. 1 pick in the 2009 NHL Draft. He has 621 points (272 goals, 349 assists) in 669 NHL games, and has scored at least 24 goals in each of his nine NHL seasons.
Tampa Bay can offer the 27-year-old a seven-year contract; New York is the only team that can offer him eight years and can sign him at any time.