Cika wannan jumla: Mueller an rubuta shi ne na 8 a cikin Phoenix Coyotes a cikin
Ƙaddamarwar NHL ta 2006. Yana wasa a matsayin cibiyar. Ya buga wasa a cikin shirin ci gaban Hockey na Amurka don kakar 2004-05 kafin ya koma Everett Silvertips na Yammacin Hockey League. Ya bi tsohon dan wasan Breck High School Blake Wheeler zuwa Coyotes, yana yin sauyi zuwa NHL a lokacin 2007-08 kakar. Saboda rawar da ya taka a farkon rabin kakar 2007-08, an zabi Mueller ya taka leda a wasan NHL YoungStars na 2008 a Atlanta. Ya zira kwallaye na farko na NHL a wasan da ya yi da Anaheim Ducks a ranar 7 ga Nuwamba, 2007.