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.

[9] 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.

[11] 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.

[13] 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.

[19] 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.

[33][34][35] In an interview, published by Kicker, Klemens Hartenbach, the sports director of Freiburg, said that how Szalai signed the contract was weird.

After the match an agreement was reached between the two clubs and Szalai signed the loan contract wearing the Hoffenheim shirt.

[46] He played all three of the team's Group F matches as a left-sided centre back as the Magyars lost to Portugal and drew with both France and Germany.

[51] He started the team's opening match of the tournament against Switzerland, playing 79 minutes of the 3–1 loss before being substituted for Márton Dárdai.

[53] On 27 August 2024, Marco Rossi did not invite him to play against Germany in the 2024–25 UEFA Nations League match due on 7 September 2024.

[55] In an interview with Nemzeti Sport, his father, also named Attila Szalai, said that in a transfer the most important factor is not the money, but being happy with the move.