Müller was born in 1740 or 1742 in the Habsburg Empire. While the Allgemeine Deutsche Biographie gives 1 July 1740 and Vienna as date and place of birth, the Neue Deutsche Biographie prefers 4 October 1742 and the small town of Poysdorf in Lower Austria. The much older works Neuer Nekrolog der Deutschen and Oesterreichische National-Encyklopädie do not give a place of birth and only the year 1740 for his birth. Even articles by Mary Elvira Weeks on the discovery of tellurium, published in the Journal of Chemical Education in 1932, and 1935 quote two different locations of his birth: one in Vienna, Archduchy of Austria and the other Hermannstadt, Principality of Transylvania (present-day Sibiu, Romania). A newer biography on the topic makes clear that date and place of birth are not definitely known.