Warner picked up a groin strain while playing the ODIs at the start of the summer.
Warner, who has been recovering from a groin strain he picked up while fielding in the second ODI of the summer in Sydney last month, is hoping to resume Test duties for his country in the second Test at the iconic MCG.
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"I am (hopeful), that's one that I never want to miss out on," Warner told Australian sports radio network 'SEN'.
"(Adelaide's) my first missed Test through injury so I'm obviously very disappointed with that."
"With the big series that it is, it's devastating to miss a Test but I know that the guys who are walking out there are going to put their best foot forward."
Closer to regaining fitness, Warner said he plans to increase the intensity of his rehab work in this period leading into the Test starting December 26.
"Hopefully I can get up and about and start running at a higher tempo," he said.
"I managed to get up to 14 kilometres an hour (8.7mph) so I've got to work towards a max of 26 to 30 kilometres an hour by next week."
"If I can run between wickets and move laterally and do some ground fielding by the end of next week, I should be ready to go. Fingers are crossed," Warner added.
(Inputs from AFP)