The Brewers are in full rebuilding mode under new general manager David Stearns, and Lucroy told the newspaper that he wants to play for a winner.
"I'm not going to sit here and say we're going to compete for the playoffs this year," Lucroy told the newspaper in a telephone interview. "If I did that, you'd call me a liar. I'd lose credibility and respect. I want to win, and I don't see us winning in the foreseeable future. I want to go to a World Series. That's what all players want. Rebuilding is not a lot of fun for any veteran guy."
Lucroy, 29, is scheduled to make $4 million next season, while the Brewers hold a $5.25 million club option on the catcher for 2017.
With his birthday coming in June, Lucroy wants to win sooner rather than later.
"It's not guaranteed that I'm going to win if I am traded, but I'm going to be a 30-year-old catcher," he said. "I can't put numbers on how much longer I'm going to play, but as players, we want to win. I don't care about the money. I just want to win. That's the bottom line."
Lucroy made it clear he isn't demanding to be traded, and if he's with the Brewers next season, he vows to give the team his all.
"If I stay with the Brewers, I'm not going to go out and dog it," he told the newspaper. "I'm not going to be a bad teammate. I'm not going to be a bad clubhouse guy. I'm not going to be bitter. It's just part of the game."
Lucroy was an All-Star in 2014, when he posted a .301 batting average and hit an NL-best 53 doubles, 13 home runs and 69 RBIs. A broken toe and concussion limited him to just 103 games last season, when he batted .264 with seven homers and 43 RBIs.
He told the Journal Sentinel he has "been getting after it" in offseason workouts and is "a lot stronger than I've been in a long time."
"I have a chip on my shoulder, and I plan on going out and showing people I'm perfectly fine," he told the newspaper.