Varnish lost her place on the team in April, sparking a furore that eventually led to the resignation of British Cycling technical director Shane Sutton amid allegations of sexism and bullying.
Sutton had told Varnish that her performances weren't up to the required level, saying: "There is no point carrying on and wasting UK Sport’s money on someone who is not going to medal going forward."
Varnish also alleges that Sutton told her to "move on and get on with having a baby". Varnish also believes that she was left out of the team after making comments during a television interview after the 2016 world championships where she criticised the GB team's selection procedure.
In a statement issued on Varnish's personal website on Tuesday, the 25-year-old said that she wants to get her place back on the GB team and can win a medal.
Varnish states that she has set up a meeting with new BC performance director Andy Harrison on her return from Australia.
"My immediate priority is to win back my place on the British Cycling team, ahead of the 2016 Olympic Games, and to prove that I was, and still am, good enough to win medals for Great Britain," wrote Varnish. "I have reached out to the new performance director at British Cycling, Andy Harrison, and will meet with him on my return to the UK.
"I still maintain that the decision not to renew my contract was not down to performance. Prior to the 2016 World Championships I was not once told that I was under-performing. We have monthly reviews and at no stage was I put under review, or set performance targets to keep my place on the programme.
"The first I knew that the coaches had an issue with my performance levels, or training data, was five days after the 2016 World Championships, when I was told I wouldn’t be getting a new contract over the phone.
"I also maintain that I am a world-class athlete, and have the ability to win more medals for Great Britain."
Varnish then details her achievements in assisting the GB squad to qualify places for the individual sprint and keirin disciplines at the 2016 Olympics – GB did not qualify for the team sprint.
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"During the two-year Olympic qualifying process I gained more qualifying points than any other British female sprint rider, I was consistently performing in the top five in the world for lap one times in the team sprint, I qualified the Olympic places for Great Britain in the individual sprint and keirin. Since 2012 I have won medals at the World and European Championships and Commonwealth Games."
According to the UCI's track ranking, Varnish is currently the top-ranked British rider in the sprint discipline. Katy Marchant and Becky James are currently front runners for GB's sprint discipline places.
"It is been a dream for me ever since London 2012 to compete and be successful in Rio," Varnish said.
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