Before telemarking, Müller was an alpine racer in the Allgäu student squad (ASV) and as a cross-country skier for the ASV and the Bavarian ski association BSV . He had to stop cross-country skiing because of a sinus infection . In 2010 he came to telemark sport through his friend and current national team colleague Benedikt Holzmann . In January 2011 he contested its first World Cup race in Bad Hindelang / Oberjoch . At the World Cup in Méribel and Rjukan , he came second in the Classic Sprint and Classic. In the overall World Cup he took eighth place, fourth place in the Classic, 13th place in the giant slalom and ninth place in the Classic Sprint. At the 2011 Junior World Championships in Hafjell he won the bronze medal in the giant slalom, the silver medal in the classic sprint, and the gold medal in the sprint and overall (giant slalom, classic sprint, classic). At the 2011 World Championships in Rjukan, he won the silver medal in the Classic, Classic Sprint and Giant Slalom he was 15th. Müller was German champion in the 2011 International German Telemark Championships in the Classic Sprint race. In the 2012 season he won the World Cup in Bohinj in the Classic Sprint, in Kvittfjell in the Classic and in Steamboat Springs in the Classic and the Classic Sprint. In the overall World Cup he took second place, in the Classic first place, in the Classic Sprint third place and in the Parallel Sprint second place. At his second Junior World Championships in Espot in 2012 , Müller won the gold medal twice. During his second participation in the International German Telemark Championships in 2012, he was again German champion in the Classic Sprint race.
In the 2013 season he was able to win three races and was among the top ten at all World Cup stations. At the World Cup in Rauris he was disqualified. In the overall World Cup he took third place, in the Classic second place, in the Classic Sprint in third place and in the parallel sprint in fifth place. As a year before, he won two gold medals at the 2013 Junior World Championships in Vallée de Chamonix and three gold medals at the 2013 World Championships in Espot . For the third time in a row he won the German Telemark Championships in 2013.
In the 2013/14 season , Müller was always among the top three from the first World Cup race in Hintertux to the finals in Rjukan, of which he won 14 races. With the exception of three World Cup races, he finished sixth in Rauris, fourth in Steamboat Springs and 17th in Rjukan. In the overall ranking and in all discipline rankings, he took first place. Again he won the gold medal at the German telemark championships in 2014. Up until the world championship he was able to win four world cups in the 2014/15 season . In the first race in Hintertux in the Classic Sprint race, he did not finish. At the 2015 World Championships in Steamboat Springs, he won the classic sprint, parallel sprint, classic and overall gold medal. After the World Championships, he came on the podium six times out of nine races. In the overall World Cup ranking he came in first place, in the Classic in third place, in the Classic Sprint in first place and in the Parallel Sprint in second place.