The Chicago Cubs, Arizona Diamondbacks and Tampa Bay Rays are the other teams trying to sign Akiyama, who announced in October he would file for international free agency with the goal of playing in the United States.
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Akiyama, 31, has played his entire career in Japan. He hit .301 with 116 home runs in nine seasons. Last season, he hit .301 with 20 home runs for Seibu.
The Reds have made headlines with two free-agent signings this offseason, adding infielder Mike Moustakas and starting pitcher Wade Miley.