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"We've been talking to clubs, but I don't think there's anything that's close," Reds president of baseball operations Walt Jocketty told the Cincinnati Enquirer. "Hopefully we get something done with somebody before the Winter Meetings. We'd like to get moving on some things."
The Winter Meetings begin Dec. 7 in Nashville.
Chapman, who turns 28 on Feb. 28, has a 2.17 career ERA and 146 saves in 164 chances with 546 strikeouts in 319 innings during his six seasons for the Reds. After he earned $8.05 million in 2015, the left-hander is eligible for arbitration for a third and final time and can be a free agent after the '16 season.
Because the Reds are rebuilding, Chapman has become a rather sizeable trade chip. Other teams seeking a closer include the Marlins, Astros, D-backs and possibly the Nationals, Mariners and Giants.
Jocketty and general manager Dick Williams are also listening for potential offers on other players, making this one of the busier offseasons Cincinnati has had for some time.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.