Team executives offered Matsui a four-year, $32 million contract to stay in the Japanese League, but Matsui has his heart set on proving himself in the majors, much like Ichiro Suzuki did with the Seattle Mariners.
"It was painful to tell my coaches, but my personal desire to go over there and play didn't go away," Matsui told the New York Daily News.
The New York Yankees are believed to be the frontrunners for Matsui, who hit .334 and led Japan's Central League with 50 homers and 107 RBI.
After their working agreement of 20 years with the Nippon Ham Fighters expired earlier this year, the Yankees forged a relationship with Yomiuri.
The Seattle Mariners, who have Suzuki and closer Kazuhiro Sasaki, will also likely make a bid for Matsui, who played for $4.7 million last season.