The 25-year-old star won gold on the track at London 2012, but, on the advice of British Cycling, switched full-time to road racing last year.
"Initially I was told I couldn't appeal," she said. "I'm going to explore that option.
"I haven't really been given a fair explanation as to why I haven't been selected, to be completely honest."
The Rio Olympics get under way on 5 August.
King is second-highest British rider in the world standings but was overlooked when the British road race team was revealed last week.
Emma Pooley and Nikki Harris were chosen instead - to support lead rider Lizzie Armitstead - despite both being ranked below her.
King called the decision "unfair" but thought she was unable to appeal against the decision because she was not on British Cycling's funded programme.
However, British Cycling's interim performance manager Andy Harrison subsequently announced she could.
"I have really enjoyed being on the road this year and I feel I've exceeded all expectations in terms of my results," said King.
"I was given nine criteria at the start of the year which I've been working toward and I'm absolutely gutted."
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King defied expectations by returning to elite racing after a life-threatening training crash in November 2014 left her with eight broken ribs, a bruised liver and punctured lung.
She stopped receiving UK Sport funding two months later and was told she would not be considered for the Rio track cycling team late last year.
She has been focusing exclusively on road racing ever since.
Despite her Olympic omission and the controversies surrounding British Cycling following the departure of technical director Shane Sutton amid claims of sexism and discrimination, King refuses to be too critical of the national set-up.
"When I was on the programme, I was supported really well," she said. "It's just disappointing that I feel like this selection hasn't been fair to me."
She insisted: "I'm not here to slag off British Cycling and I do wish all of the British riders a lot of success in Rio."

The latest saw NHS Orkney's headquarters at Garden House broken into overnight on Tuesday, with property stolen.
The spate of incidents happened within the space of a week.
Police in Kirkwall are appealing for anyone with information to contact them.
Olympic champion Dani King may appeal against British Cycling's decision not to select her for the Rio Games.
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Police in Orkney are investigating a spate of break-ins and attempted break-ins in Kirkwall.