Müller played his domestic league debut for his new club in the away game on 5 September 1943 as Basel drew 1–1 with Luzern.
[1] Müller spent fourteen years between the posts for RotBlau, mainly as their first choice goalkeeper, playing in total 380 matches.
In addition to this title, Müller also reached the Swiss Cup final twice, one victory and one defeat.
At the end of the 1943–44 cup season, on 10 April 1944 in the Wankdorf Stadium in Bern, Basel were defeated in the final by Lausanne Sport through three goals scored in the last five minutes.
[3] Müller never made it to an appearance in the Swiss national football team, however, he was in the squad for more than five years as their substitute goalie.