A poll of 800 11- to 19-year-olds was carried out by the Youth Sport Trust, the umbrella body for specialist sports colleges.
More than four out of 10 said they wanted to do volunteer work at the Olympics, but just one in 10 were keen to give up their time to help with the tennis at Wimbledon or the rugby and cricket world cups.
The figures were released as the trust began its search for the next generation of football referees and cricket umpires at the UK's largest camp for youth volunteers.
The Step into Sport camp, held this week at Loughborough University, gave 400 16- to 19-year-olds the chance to complete coaching awards and entry-level qualifications to get them on to the officiating ladder.
Dame Kelly Holmes, the Olympic champion athlete, and Hope Powell, the England women's football coach, joined the group.
Phil Veasey, the head of national investment at Sport England, said: "These camps are an excellent way of motivating young people, giving them confidence to succeed and unleashing their full potential."