King, 25, won Olympic gold in the team pursuit at London 2012 but, on the advice of British Cycling, switched full-time to road racing last year.
"Initially I was told that I couldn't appeal as I wasn't a programme rider," King, the second-highest British rider in the world standings, told BBC Sport.
"I'm going to explore that option."
King was overlooked when the GB squad was revealed last week but British Cycling's interim performance manager Andy Harrison later revealed athletes outside its funded programme could now appeal.
