Born in Ilion, a district in west Athens, Greece, Siatounis began his career at Panathinaikos' youth academy in 2011, staying there for eight years.[2] In 2018 he moved to Italy,[2][3] joining Sampdoria's under-17 team for a fee of €150,000.[4] After playing with the under-18s, in the 2020–21 season Siatounis helped Sampdoria reach the semi-finals with the Primavera (under-19) team,[3] scoring six goals and making seven assists.[5]
Monza
Following the expiration of his contract with Sampdoria on 30 June 2021,[3] Siatounis joined Serie B side Monza on a three-year contract.[6] He made his unofficial debut on 15 July, as a substitute in a 14–0 friendly win against Real Vicenza.[7] Siatounis scored five days later, in Monza's second pre-season friendly against Anaune Val di Non, which ended in a 5–0 win.[8]
On 1 November, Siatounis made his official debut for Monza, coming on as a substitute against Alessandria in a 1–0 Serie B win.[9]
Virtus Entella
On 2 January 2023, Siatounis joined Serie C club Virtus Entella, with Monza holding a buy-back clause.[10]