Müller began his motorsport career in karting in 2004 , in which he was active until 2009. In 2010, Müller switched to formula racing and started for Eifelland Racing in the ADAC Formula Masters . He regularly scored points and finished his debut season in ninth place in the drivers' championship. In 2011 he contested his second ADAC Formula Masters season for ma-con Motorsport . He won four races and achieved twelve podium finishes. At the end of the season he was in second place behind the champion Pascal Wehrlein . However, the ranking at the end of the season was provisional due to an appeal hearing. In February 2012 the decision of the appeal hearing was announced and Müller was removed from the ranking in a race he had won. As a result, he fell back to third place behind Emil Bernstorff .
In 2012 Müller started for the Prema Powerteam , which won the championship title in 2011, in the Formula 3 Euro Series . In 2012 , Müller was also eligible for the European Formula 3 championship . With two victories in the Formula 3 Euro Series, he reached sixth place. He was eighth in the European Formula 3 championship. In both series, the championship title went to his team-mate Daniel Juncadella . In 2013 , Müller started for ma-con and later for Van Amersfoort Racing in the European Formula 3 championship. Müller once stood on the podium in third place and finished the season in ninth place overall.
In 2014 Müller left formula racing and switched to GT racing. He competes in the German Porsche Carrera Cup . In addition, he was accepted into the Porsche sponsorship program.
Müller celebrated his very first win of the season in July 2015. In the Porsche Mobil 1 Supercup at the Hungaroring near Budapest, he already prevailed in qualifying and achieved a lead of 6.1 seconds after 14 laps. His overall second victory at the Supercup.