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Maeda, 27, has pitched for the Carp since 2008, going 97-67 with a 2.39 ERA in that span. He has twice been named the winner of the Sawamura Award, given to the league's top pitcher.
According to the report, Carp general manager Kiyoaki Suzuki "indicated the pitcher's request might be granted" after turning him down each of the past two seasons.
"If we decide on a course of action around the end of next week, I think that will work," Suzuki said Tuesday.
In 29 starts this season, Maeda went 15-8 with a 2.09 ERA and 175 strikeouts in 206 1/3 innings.
"I want to go while I'm still young, and I want to win a championship with the Carp. While I've gone back and forth between those two goals, my desire to go has not lessened, and in fact has become even stronger," Maeda said.
Maeda helped to lead Japan to a third-place finish in the WBSC Premier 12 tournament last week.
According the current posting rules, which went into effect in 2013, a Japanese team must set a release fee on a player that can be no higher than $20 million. Beginning the day after the player is posted, and concluding 30 days later, any MLB club willing to pay the release fee may negotiate with the player in an attempt to reach a deal.
While Maeda has put up stats in Nippon Professional Baseball that compare favorably to the likes of Masahiro Tanaka and Yu Darvish, his slight frame (he's listed at 6-foot, 154 pounds) and average fastball velocity (he sits in the low 90s) suggest that he won't command a contract commensurate with an ace, even if his release fee is the maximum $20 million.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.