On May 2, 2019, Vennaro signed with the Ottawa Champions of the Can-Am League.[3] In 10 outings for the club, Vennaro recorded an 0.77 ERA with 16 strikeouts across 11+2⁄3 innings pitched.[4]
Milwaukee Brewers
On June 19, 2019, Vennaro signed a minor league contract with the Milwaukee Brewers.[5] He spent the remainder of the year with the rookie–level Arizona League Brewers, for whom he had a 3.86 ERA over 28 innings.[6] Vennaro did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[7]
He spent the 2021 season playing with the Double–A Biloxi Shuckers where he made 37 relief appearances and went 1-3 with a 7.61 ERA, 50 strikeouts, and 23 walks over 36+2⁄3 innings.[8] Vennaro opened the 2022 season with Biloxi and was promoted to the Triple–A Nashville Sounds in late May.[9] Over 49 relief appearances between the two teams, he went 6-2 with a 5.47 ERA, 56 strikeouts, and 11 saves over 54+1⁄3 innings.[10]
Vennaro spent the entirety of the 2023 season with Double–A Biloxi, registering a 6.05 ERA with 47 strikeouts and 4 saves across 41 relief outings. On September 17, 2023, Vennaro was released by the Brewers organization.[11]
Gastonia Baseball Club
On April 18, 2024, Vennaro signed with the Gastonia Baseball Club of the Atlantic League of Professional Baseball.[12] In nine games for Gastonia, he struggled to a 7.36 ERA with 12 strikeouts and 2 saves across 7+1⁄3 innings pitched. On June 5, Vennaro was released by the club.[13]