Aleksandar Stanković

Whilst he was captaining the Serbia U17 team to the semi-finals of the 2022 UEFA European Under-17 Championship, Stanković was described by the UEFA website as having set-piece delivery that would "be a menace to any opponent" and "a blend of finesse and fight in midfield [which] makes it clear why he wears the captain's armband".

Inter Milan

On 1 October 2022, Stanković made his debut in the Inter Milan first team match day squad, being named on the substitute bench in Serie A match against Roma at the San Siro. He was part of the match day squad, but an unused substitute, as Inter won the 2022–23 Coppa Italia title with a 2–1 victory over Fiorentina.

Loan to Luzern

On 3 July 2024, Stanković joined Swiss Super League club Luzern on a season-long loan, with an option to buy and a buyback clause in favour of Inter. The same on 26 October, he scored his first goal in a 3–2 defeat against Yverdon Sport.

Club Brugge

On 24 July 2025, Stanković officially joined Belgian Pro League side Club Brugge, signing a contract until 2029. Inter Milan maintained a buyback option to sign Stanković for €22m in 2026 and €25m in 2027. One month later, on 27 August, he scored his first goal for the club in a 6–0 victory against Rangers in the second leg of the Champions League qualifying play-off round.

Return to Inter Milan

On 5 June 2026, Inter Milan exercised their €23 million buy-back clause to re-sign Stanković, who subsequently signed a contract with the club until 2031.

In February 2020, Stanković was called up to the Serbia U15 squad. He represented Serbia under-16 and Serbia U17, and became captain of the youth team for the first time in May 2021. Stanković served as captain to the Serbian team that reached the semi-finals of the 2022 UEFA European Under-17 Championship. He received his first call-up in September 2022 and played as captain for the Serbia U18 national team in a 1–0 defeat against Italy U18. Against the same opponent four days later, he scored the first goal in a 2–1 win for his country.

His brother Filip plays as a goalkeeper for Venezia. They are both sons of former Inter and Serbian international footballer Dejan Stanković. His mother Ana is Slovenian, and the family spend some time in Ljubljana. His maternal uncle is a Slovenian former professional footballer Milenko Ačimovič. On 11 October 2025, Stanković debuted for the Serbian senior team in a 0–1 2026 FIFA World Cup qualification home loss against Albania.