At the 2021 Australian Open Müller won his first Grand Slam match as a lucky loser defeating Juan Ignacio Londero.

At the 2023 Qatar ExxonMobil Open in Doha, Müller as a qualifier reached his first ATP quarterfinal in his career, defeating Nikoloz Basilashvili and eighth seed Botic van de Zandschulp.

[6] At the 2023 Grand Prix Hassan II he reached a second quarterfinal defeating sixth seed Richard Gasquet and Francesco Passaro.

[7] He then faced Russian Pavel Kotov, defeating him also in two hours in straight sets to reach his first ATP final, before losing to Roberto Carballes Baena.

[8] He made his Masters debut at the 2023 Italian Open (tennis) as a qualifier and recorded his first win defeating Kyle Edmund.

Following a quarterfinal showing as a qualifier at the 2024 ASB Classic where he defeated compatriot Benjamin Bonzi and third seed Francisco Cerúndolo, he reached the top 75 in the rankings on 15 January 2024.

[citation needed] In February, Muller lost to Andy Murray in the first round of the ATP Qatar Open.

[18] In July, he won his first Challenger title in more than a year in San Marino, defeating Tseng Chun-hsin in the final.

[19][20] He received a wildcard for the main draw of the US Open,[21] where he reached the second round, losing to fourth seed Alexander Zverev.