He previously played in the National Hockey League (NHL) with the San Jose Sharks and the New Jersey Devils from 2014 to 2020.

As a youth, Müller played in the 2008 Quebec International Pee-Wee Hockey Tournament with the Swiss Eastern team.

[7] On 27 February 2019, Müller was stretchered off the ice due to an injury sustained in a New Jersey home game against the Calgary Flames.

[9] Müller played for Switzerland in the 2013 World Junior Ice Hockey Championships in Ufa, Russia.

Ahead of the tournament, Müller said, "I'm looking forward to playing against the best players in junior hockey, especially the Canadians, Americans, Swedes and the other top nations.