MLB.com's Joe Frisaro first suggested the potential deal on Wednesday.
On Tuesday, the Reds decided Olivo would not be on their Opening Day roster. Olivo, a non-roster invitee, was offered a $100,000 retention bonus to go to Triple-A Louisville, but opted to test the market.
Olivo is an 11-year veteran who played with the Marlins from 2006-07. He is a .241 career hitter who has spent time with the White Sox, Mariners, Padres, Royals, Rockies and Mariners.