Gaudino, is a youth product of the Bayern Munich Academy. He was promoted to the first team for the 2014–15 season after impressing Pep Guardiola. On 13 August 2014, he made his first-team debut in the German Supercup, playing the full 90 minutes as Bayern lost 0–2 against Borussia Dortmund. He made his league debut in the first match of the 2014–15 Bundesliga season as a starter against VfL Wolfsburg. Bayern won the match 2–1, and Gaudino became the fourth youngest debutant in the club's history. Gaudino made his Champions League debut on 10 December 2014 in a 3–0 home win against CSKA Moscow. For the 2015–16 season, he played for the reserve team where he made 19 appearances.