Muller was a professional tennis player in 1985 and was the following year in the semifinals of the Challenger tournament in Jerusalem, which he won in the doubles competition. He won two individual titles on the Challenger tour, but specialized mainly on the men's doubles. His first doubles title on the ATP World Tour, he reached in 1987 on the side of Gary Donnelly in Schenectady. During his career he won a total of eight double tournaments. In addition, he was in twelve finals, including at the Masters Series Cincinnati, Indian Wells and Stockholm. Its highest listing in the tennis world ranking he reached in 1990 with position 49 in the singles and in 1993 with seven position in the doubles.
His best individual result at a Grand Slam tournament was reaching the third round at the Australian Open and the U.S. Open. In the doubles competition, he reached the semi-finals of the Australian Open, Wimbledon and the U.S. Open.
Muller played between 1995 and 1996 two double batches for the South African Davis Cup team, his record was 1-1. In the quarter-final defeat against Russia he lost the doubles match on the side of Wayne Ferreira, his second and last double he won in the first round game against Austria.