Muller became a professional tennis player in 1985 and was in the semifinals of the Challenger tournament in Jerusalem the following year , which he won in the doubles competition. He won two singles titles on the Challenger Tour, but mainly specialized in the men's doubles. He achieved his first double title on the ATP World Tour in 1987 at the side of Gary Donnelly in Schenectady . In the course of his career he won a total of eight doubles tournaments. He was also in twelve finals, including the Masters tournaments in Cincinnati , Indian Wells and Stockholm . He reached his highest ranking in the tennis world rankings in 1990 with position 49 in singles and in 1993 with position seven in doubles. Muller played his last professional match together with his doubles partner Marcos Ondruska in September 1997 at the Grand Prix in Bournemouth.
His best individual result in a Grand Slam tournament was reaching the third round at the Australian Open and the US Open . In the doubles competition he reached the semifinals of the Australian Open, Wimbledon and the US Open.
Muller played two doubles games for the South African Davis Cup team between 1995 and 1996 , his record was 1-1. In the quarter-final defeat against Russia , he lost the doubles encounter alongside Wayne Ferreira , and he won his second and last double in the first round match against Austria .