Early career Šeško began his career at his hometown club Radeče when he was in the first grade. He then spent one year with
Rudar Trbovlje in the under-11 selection, before returning to Radeče. In the 2017–18 season, he scored 59 goals in 23 matches for the under-15s. He debuted with Red Bull Salzburg in a 3–0
Austrian Football Bundesliga win over
TSV Hartberg on 30 January 2021.
Loan to FC Liefering Immediately after signing with Red Bull Salzburg, he was moved to their farm club
FC Liefering, competing in the
Austrian Second League. In the
2020–21 season, he scored 21 goals in 29 appearances and became the league's second-best goalscorer. He scored most of his goals in the final part of the season, scoring 13 goals in the last 7 rounds.
RB Leipzig On 9 August 2022,
RB Leipzig announced that Šeško would join them on 1 July 2023, on a five-year contract until 2028, for a reported transfer fee of around €24 million. On 3 September 2023, Šeško scored his first goals for RB Leipzig by netting a brace in a 3–0 away win over
Union Berlin, which ended their 24-match streak without loss at home. On 19 September, he scored his first
UEFA Champions League goal (excluding qualifying rounds) as RB Leipzig defeated
Young Boys 3–1 away from home in the matchday 1 of the
2023–24 edition. Šeško finished his first season with 18 goals across all competitions, and also became the youngest ever player to score in seven consecutive
Bundesliga games at 20 years and 353 days. In June 2024,
Arsenal,
Chelsea,
Manchester United and
AC Milan all pursued Šeško, but he decided to stay with RB Leipzig, extending his existing contract by another year until 2029. During the
2024–25 season, he emerged as RB Leipzig's top scorer, setting a personal record with 21 goals in all competitions.
Manchester United On 9 August 2025,
Premier League club Manchester United announced the signing of Šeško on a five-year contract until 2030, thus becoming the first-ever Slovenian to represent the club. The transfer fee was reported to be an initial €76.5 million, with an additional €8.5 million in performance related add-ons. On 17 August, he made his debut for the club, as a substitute, in a 1–0 loss against Arsenal in the opening round of the Premier League. A month later, on 27 September, he netted his first goal for the club in a 3–1 away defeat against
Brentford. In the first part of the 2025–26 season, Šeško scored just twice in 16 appearances under manager
Ruben Amorim. However, at the beginning of January 2026, Amorim was dismissed from the head coach role of Manchester United and was replaced by interim manager
Darren Fletcher in the short term, then
Michael Carrick for the rest of the season. The managerial change coincided with Šeško entering a strong goalscoring run, with six goals throughout the months of January and February, which included stoppage time goals against
Fulham and
West Ham. ==International career==