Early years

Born in Wunstorf, Hanover Region,^[2] Kühn began playing football at TSV Klein Heidorn and 1. FC Wunstorf,^[3] before joining the youth academy of FC St. Pauli, where he played for two years.^[1][4] In 2011, Kühn moved to Hannover 96, where he joined the U13 team. In the 2014–15 season, at the age of 15, he had already made two appearances for their U17 team in the Under 17 Bundesliga.^[5] For the 2015–16 season, Kühn moved to the U17 team of RB Leipzig,^[6] for whom he scored 18 goals in 22 appearances in the Under 17 Bundesliga. In the 2016–17 season, the striker scored 6 goals in 13 matches in the Under 17 Bundesliga, but fell out with a high ankle sprain. Upon his return for the second half of the season, he was already a part of the team competing in the Under 19 Bundesliga.^[1] In the 2017–18 season he was permanently moved up to the U19-team, for whom he also competed in the UEFA Youth League, and regularly trained with the first team.^[7]

Ajax

Kühn signed for Dutch club Ajax from RB Leipzig in January 2018 for a fee of €2 million.^[8] He became part of the second team, Jong Ajax, making 5 appearances in the second-tier Eerste Divisie in the 2017–18 season as the team became league champions. He was also utilised for the U19-team. In the 2018–19 season, Kühn made 21 appearances in the Eerste Divisie, in which he scored 5 goals. He also made 6 appearances for the U19s in the UEFA Youth League, in which he scored 6 goals, and 5 appearances in the domestic under-19 league, where he scored 2 goals. In the first half of the 2019–20 season, Kühn made 17 Eerste Divisie appearances in which he scored 3 goals.^[2]

Bayern Munich

In January 2020, Kühn moved on loan to FC Bayern Munich for six months.^[9][10] The move was made permanent on 14 July 2020, when Kühn signed a three-year contract and was placed in the reserve team Bayern Munich II.^[11][12]

In June 2021, Kühn moved on loan for the 2021–22 season to Erzgebirge Aue, with an option to purchase, however the team was relegated and did not activate the option.^[13][14]

Rapid Wien

In May 2022, Kühn left Bayern Munich, and joined Austrian Bundesliga club Rapid Wien for a €500,000 reported fee.^[15]

Celtic

On 16 January 2024, Kühn signed a five-and-a-half-year contract with Scottish Premiership club Celtic, for a fee reported to be around £3 million.^[16][17][18]