Johnson, 33, has bowled long spells during the first three Tests against India, and has said he is hoping for a more responsive pitch in the fourth which begins in Sydney on Tuesday.
"Definitely, all us bowlers feel like we need to have a bit of a freshen up," he said on Friday. "So we'll just see what happens after this match here.
"And then we've got some tri-series one-dayers, so hopefully I can get a bit of a break at some stage there."
Johnson missed a training session with the rest of the team on Saturday, Australian Associated Press reported, adding that he had stayed instead at their hotel for treatment.
Australia's squad includes fellow left-armer Mitchell Starc and Peter Siddle as potential back-up pace bowlers — along with Ryan Harris and Josh Hazlewood.
Harris has said he is planning on playing in Sydney, and if Johnson is rested he could be replaced by Starc.
"We haven't trained for a couple of days, so I am raring to get out there today and in the next couple of days, in order to get myself best prepared for this Test," said Starc Saturday.
"I guess it [selection] depends on the fitness of other blokes and how they have pulled up from last week."
"The decision isn't up to me, but If I am called up this week I will be ready."
Australia regained the Border-Gavaskar Trophy on Tuesday after India hung on for a tense draw in the third Test in Melbourne.
Australia won the first two Tests in Adelaide and Brisbane.
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