Konta, 28, plans to be on a plane Down Under on December 30, but said the tendonitis-type problem has been an issue, even though she has soared in the rankings in 2019.
“I can only listen to my body,” Konta, who is currently ranked 12th in the world, said.
“I’m not giving myself any deadlines. I will be ready when I’m ready.”
Konta was ranked 38th at the start of 2019 and went close to falling out of the top 50 for the first time since October 2015 – before rediscovering her form on clay in Paris.
She lost to unseeded Czech teenager Marketa Vondrousova in the semis at Roland Garros, but then reached the quarter-finals at Wimbledon and the US Open.
Konta has not played since losing to Ukrainian fifth seed Elina Svitolina in New York in September.
“I have been carrying a knee problem since the first week of the year and it was basically a case of just managing it through the season,” Konta told reporters in London.
“Once we got to the grass it got worse, and then at the US Open it felt significantly worse.
“I have definitely booked my flight and I want to be on that plane. I am certainly hopeful that I will be ready.”
She hopes to play Brisbane and Adelaide before Melbourne on 20 January.
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