Wood is expected to throw a bullpen session Tuesday and then begin his rehab stint two days later against Toledo at 7 p.m. in Louisville.
Wood, one of key pieces in the blockbuster trade with the Los Angeles Dodgers in December, has been on the injured list all season with a lower back strain.
Wood threw 21 pitches in live batting practice Monday at Great American Ball Park and threw 42 pitches in another live batting practice session Saturday in Milwaukee, where the Reds are playing a four-game series.
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If or when Wood returns to the big leagues, the Reds will have to decide where he fits into the starting rotation. Their starters rank second in the National League with a 3.66 ERA.
Anthony DeSclafani (4-2, 4.22) has the rotation's highest ERA but is 2-0 with a 1.69 ERA in three starts in June. Tyler Mahle, the least experienced member of the staff, could be the one to lose his spot to Wood. He's 2-7 with a 4.17 ERA.