Early years Szalai started playing football in
Göd, then moved to youth team of
Vác FC and later to the youth team of
Vasas's academy,
Rapid Wien In 2012,
Austrian Bundesliga club
Rapid Wien called Szalai up, and, after a week of trials, he was signed. First, he played in the club's youth and reserve teams, in the third division, and then he was promoted to the senior team. He made his debut as a professional at the age of 18 on 11 May 2016, starting in a 1–1 home tie against
Altach. It was the only time Szalai played for the team in a professional match.
Mezőkövesd On 1 July 2017, Szalai signed a three-year contract with
Mezőkövesd. On 30 July 2017, he debuted in a 5–0 defeat against
Ferencvárosi TC at the
Ferencváros Stadion in the
2017–18 Nemzeti Bajnokság I season. In his two seasons in the Hungarian top flight, he scored two goals in 45 matches for the club. On 21 July 2018, he scored the second goal in a 3–1 victory over
Paksi FC in the
2018–19 Nemzeti Bajnokság I season at the
Mezőkövesdi Városi Stadion. He scored his second goal in a 1–1 draw with
Újpest FC at the
Szusza Ferenc Stadion on 18 August 2018.
Apollon Limassol On 1 July 2019, Szalai signed a four-year contract with
Cypriot team
Apollon Limassol. Szalai made his debut in Cyprus on as a half-time substitute in Apollon's
UEFA Europa League qualifying match against
Kauno Žalgiris, which his team won 2–0, on 11 July 2019. He then scored his first goal for his new team in the second leg of the tie on 18 July. In November 2020, Turkish club
Galatasaray inquired about signing Szalai.
Fenerbahçe On 17 January 2021, Szalai signed a four-and-a-half-year contract with
Fenerbahçe. On 25 January 2021, he made his debut for the club in a
Süper Lig match against
Kayserispor at the
Ülker Arena, which Fenerbahçe won 3–0. On 8 March 2021, Szalai scored his first goal in the Süper Lig against
Konyaspor, at the
Konya Büyükşehir Stadium, on the 29th matchday of the
2020–21 Süper Lig season; Fenerbahçe won 3–0. On 28 February 2022, Szalai scored his first and only goal in the
2021–22 Süper Lig season against
Kasımpaşa, at the
Recep Tayyip Erdoğan Stadium in
Istanbul. The match ended with a 2–1 victory for Fenerbahçe. In the
2022–23 Süper Lig season, Szalai played 32 matches and scored two goals. He scored his first goal of the season in a 4–0 victory against
Konyaspor on 25 February 2023. On 10 April 2023, he scored in a 2–1 away victory against
Fatih Karagümrük at the
Atatürk Olympic Stadium,
Istanbul. On 11 June 2023, Szalai won the
2023 Turkish Cup final with Fenerbahçe. In the final, his club beat
İstanbul Başakşehir 2–0. Although he was linked with a move to
Union Berlin during the early summer of 2023, Szalai was instead purchased by fellow German club
TSG Hoffenheim.
TSG Hoffenheim On 24 July 2023, Szalai joined TSG Hoffenheim on a four-year contract deal, for a fee of €12.3 million. On 19 August 2023, Szalai debuted against
SC Freiburg in a 2–1 home defeat in the
2023–24 Bundesliga season. He also scored an own goal in the 39th minute. Consequently, he was substituted at half time and did not feature in the starting line-up for the club's subsequent match against
1. FC Heidenheim. On 2 September, Szalai played against
VfL Wolfsburg, and was not substituted. On 13 November 2024, he played in a friendly match against
TSV Steinbach Haiger, after
Pellegrino Matarazzo was sacked by Hoffenheim.
Loan to SC Freiburg On 21 January 2024, Szalai was loaned to
SC Freiburg for the remainder of the
2023–24 Bundesliga season. In an interview, published by
Kicker, Klemens Hartenbach, the sports director of Freiburg, said that how Szalai signed the contract was weird. On 21 January 2024, Freiburg hosted Hoffenheim and Szalai was sitting among the substitutes for the entire match. After the match an agreement was reached between the two clubs and Szalai signed the loan contract wearing the Hoffenheim shirt. On 27 January 2024, he played his first match in a 3–1 defeat from
SV Werder Bremen. He entered the pitch in the 71st minute as a substitute for
Lukas Kübler. On 12 May 2024, it was announced that Freiburg would terminate his contract.
Loan to Standard Liège On 12 January 2025, he was loaned to
Belgian Pro League club
Standard Liège. On 26 January 2025, he debuted in a 1–0 victory over
F.C.V. Dender E.H. on the 23rd game week of the
Belgian Pro League. He entered the pitch in the 84th minute as a substitute for
Dennis Eckert. On the 26th game week, he was included in the starting lineup against Genk. Szalai was not substituted; however, the result was a 2–1 defeat against the leaders of the
2024–25 Belgian Pro League.
Loan to Kasımpaşa On 11 July 2025, Szalai moved on a new loan to
Kasımpaşa in Turkey. He debutted in a 2–1 defeat from
Antalyaspor in the
2025–26 Süper Lig season on 9 August 2025.
Loan to Pogoń Szczecin On 27 January 2026, Szalai joined
Pogoń Szczecin in Poland on loan. == International career ==