Müller began 2015 at the Aircel Chennai Open, where he made the quarterfinals, losing to eventual champion Stan Wawrinka. He then competed in the Sydney International losing in the semifinals to Viktor Troicki, the eventual champion. He put together his best Australian Open campaign to date, losing in the fourth round to world No. 1 and eventual champion Novak Djokovic (4–6, 5–7, 5–7). His performance during the entire month saw him crack the top 40 for the first time in his career on 2 February.