Kecskemét Szalai joined the football academy of
Kecskemét in 2010. He has been playing for the club's first team since the 2019–20 season. On 24 June 2022, he renewed his contract with Kecskemét.
2022–23 season On 8 April 2023, he scored his first goal in the
2022–23 Nemzeti Bajnokság I season against
Puskás Akadémia FC in a 3–0 victory at the
Pancho Aréna,
Felcsút. On 28 April 2023, he scored a goal in a 3–2 defeat against
Paksi FC at the
Széktói Stadion on game week 29. On 13 May 2023, he scored his third goal in the season in a 2–0 victory against reigning champions
Ferencvárosi TC on game week 31.
2023–24 season On 7 August 2023, he scored his first goal in a 3–1 victory over
Kisvárda FC in the
2023–24 Nemzeti Bajnokság I season at the
Széktói Stadion. On 13 August 2023, he scored the winning goal against
Fehérvár FC at the
Széktói Stadion. He scored his third goal in
Szusza Ferenc Stadion on 21 October 2023 in 5–3 defeat against
Újpest FC on game week 10. On 26 November 2023, he scored his fourth goal in the season in a 3–3 draw against
Fehérvár FC at the
Sóstói Stadion. On 4 January 2023, it was rumored that the club received an offer from a club to purchase his rights to play.
Lausanne On 7 January 2024, he was signed by
Swiss Super League club
FC Lausanne-Sport. On 20 January 2024, he debuted in a 1–0 defeat against
FC St. Gallen at the
Stade de la Tuilière. On 28 January 2024, he received a yellow card in a 2–1 defeat against
Luzern at the
Swissporarena in the
2023–24 Swiss Super League season.
Ferencváros On 31 August 2024, he was signed by
Nemzeti Bajnokság club
Ferencvárosi TC. On 12 April 2025, he scored his first goal in a 2–0 victory over
Zalaegerszegi TE at the
ZTE Arena in the
2024–25 Nemzeti Bajnokság I season. On 27 April 2025, he scored his second goal in a 3–2 victory over
MTK Budapest FC at the
Hidegkuti Nándor Stadion. On 10 May 2025, he also scored an important goal in a 3–2 away victory over
Paksi FC. Szalai won the
2024–25 Nemzeti Bajnokság I season with Ferencváros after beating
Győr 2–1 at the
ETO Park on the last match day on 24 May 2025.
2025–26 season On 12 August 2025, he scored a goal in a 3–0 victory over
PFC Ludogorets Razgrad at the
Groupama Aréna in the third round of the
2025–26 UEFA Champions League qualifying. On 19 December 2025, he scored a goal in a 1–0 victory over
Diósgyőri VTK at the
Diósgyőri Stadion. == International career ==