The Spinners are expected to make an announcement Friday. Burton Rocks, Oliver's agent, confirmed the hiring.
Oliver, 48, hit .247 with 102 career home runs over 13 seasons with the Reds, Brewers, Tigers, Mariners, Pirates, Yankees and Red Sox. He was the starting catcher on Cincinnati's wire-to-wire World Championship team in 1990.
Oliver had been out of pro ball since his retirement as a player in 2001. He coached a high school team near his home in Orlando, Fla., in 2011.