Ozuna said on Thursday he is following the advice of his agent, Scott Boras.
"[Boras] tells me 'Don't hurry. Be waiting for the moment, and let's see what happens in a couple of years,'" Ozuna said before the Marlins faced the Braves on Thursday.
In the offseason, the Marlins made preliminary contact with Ozuna's camp, expressing their desire to explore an extension.
The Marlins did the same with left fielder Christian Yelich, right-hander Jose Fernandez and shortstop Adeiny Hechavarria.
On Wednesday, Miami and Yelich reached agreement on a seven-year, $49.570 million deal. An official announcement is expected on Sunday.
In November, the Marlins signed right fielder Giancarlo Stanton to a record 13-year, $325 million deal.
The Marlins feel they have the best outfield trio in the National League, and they'd like to keep them around for the foreseeable future. Ozuna is eligible for free agency in 2020. So, the club could still retain its current outfield at least five more seasons.
"The exciting part is these guys are going to continue to get better," manager Mike Redmond said. "That's fun. To see what these guys can possibly become down the road is going to be fun to watch."
All three are home grown, with Ozuna signing as a 17-year-old from the Dominican Republic in 2008.
In 2014, his first full big league season, Ozuna batted .269 with 23 home runs and 85 RBIs.
"We talk a lot [with Boras]," Ozuna said. "He says 'Don't worry. Don't worry. Worry about your hitting and play the game. I'll worry about your career and your money. That's what he says.' If he made a good deal with the team, I agree.
"Let's see what happens next year. I don't want something in my head, like a distraction. I'm just going to play the game, and that's it. Try to have a good season and if we get a championship, that's what we want. I'm gonna play and do my best."