King is expected to return to Australia's side for Tuesday's opening one-dayer against India in Brisbane, after being overlooked for the three T20s against the tourists.
The hosts must win at least two of the three ODIs against India if they are to have any chance of lifting the multi-format trophy next month.
Australia's best bowler at last year's ODI World Cup, King has played just five T20s in the past three years, while largely being stuck behind fellow leggie Georgia Wareham.
Her chances of returning to the side have also taken another hit, with finger-spinner Sophie Molineux now locked in as a fixture in the side as captain.
T20 cricket will be a priority for Australia over the next period, with two World Cups, an Olympics and Champions Trophy coming up before the end of 2028.
And King is adamant she doesn't want to be on the sidelines through that stretch, particularly given the 30-year-old is bowling as well now as any point in her career.
"I'm not going to probably just succumb to, okay, I'll just play ODIs," King told AAP.
"There's some serious hunger in me to be a multi-format player because we play so much of it in the women's game.
"With T20 World Cups around multi-format series, it's something that I don't ever see myself not trying to get to.
"There's always disappointment when you get left out of squads and teams, but it gives me a bit more fire in the belly to do everything I can."
King is considered to be better suited to ODIs and Tests as a more attacking spinner, with her big-turning legbreaks earning her 13 wickets at 17.38 in last year's World Cup.
Wareham's tighter bowling has then seen her as a preferred option in T20s, while the 26-year-old's batting is also considered valuable.
"People keep talking about you can't play two legsinners, but Wolfy (Wareham) and I have played many games together in different formats," King said.
"I've just got to put head down, ass up, get to work and keep taking opportunities when I can.
"My desire to do well, not just for myself, but for Australia as well, is always going to be there."
King also remains confident her spin can be a threat in T20 internationals, having taken 27 wickets at 18.81 in the format for Australia.
"I know naturally I'm a quicker leg-spinner, but because I still get grip and turn, I don't need to really change anything for T20s," King said.
"What I've grown in the T20 space is the tactical side of the game. You have to think a lot quicker.
"You've only got four overs, so you have less time to work out a batter..
"I don't think you lose your skill overnight, and the selectors know that as well."
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