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.[3] It was the only time Szalai played for the team in a professional match.[4]
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.[10]
Fenerbahçe
On 17 January 2021, Szalai signed a four-and-a-half-year contract with Fenerbahçe.[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.[12]
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.[20][21]
TSG Hoffenheim
On 24 July 2023, Szalai joined TSG Hoffenheim on a four-year contract deal, for a fee of €12.3 million.[22][23][24]
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.[25] 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.[26] On 2 September, Szalai played against VfL Wolfsburg, and was not substituted.[27][28]
On 21 January 2024, Szalai was loaned to SC Freiburg for the remainder of the 2023–24 Bundesliga season.[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. 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.[36][37] On 27 January 2024, he played his first match in a 3–1 defeat from SV Werder Bremen.[38] 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.[39]
On 1 June 2021, Szalai was included in the final 26-man squad to represent Hungary at the rescheduled UEFA Euro 2020 tournament.[41] 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.[42]
On 14 May 2024, Szalai was named in Hungary's squad for UEFA Euro 2024.[46] 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.[47] After being an unused substitute in the second match against Germany, he appeared as a 74th minute substitute for Dárdai in the 1–0 win over Scotland that ensured Hungary would finish third in Group A.[48]
Szalai is the third most popular sportsperson in Hungary, based on followers on Instagram.[50]
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.[51]
On 27 December 2022, he played an important role before the match against Hatayspor by holding a picture of a 6-year-old boy who suffers from Leukemia.[52] In this way, Mustafa Roni Güclü could 'participate' in the match.