Finnegan was added to the Reds' 60-man player pool Friday.
Finnegan wasn't included in the initial group of players and missed out on summer camp, but he'll head to the alternate training site to begin participating in workouts. The 27-year-old hasn't appeared in the majors since 2018, when he had a 7.40 ERA, 2.03 WHIP and 14:15 K:BB over 20.2 innings (five starts).