Zeki Amdouni represented Servette, Meyrin, Étoile Carouge, and Stade Lausanne before making his debut in the Swiss Super League in the 2021/22 season with the shirt of Lausanne-Sport.
This was followed by a loan move to Basel, where in the 2022/23 season, he scored 22 goals in 52 matches, becoming one of the top scorers of the Conference League with seven successful shots, all in the knockout phase of the competition. Amdouni's performance caught the attention of Burnley, who signed him permanently from Lausanne-Sport for the 2023/24 season, as the club returned to the Premier League.
Son of a Turkish father and a Tunisian mother, the forward had previously played one match with Turkey's U-21 team before choosing to represent Switzerland, making his senior team debut on September 28, 2022. Amdouni was part of the 26 selected players for Switzerland in the 2024 UEFA European Championship, where he participated in four matches.