Gillespie broke down with a groin muscle strain during the second Test of the four-match series against India earlier this month and was rested for the third Test, which Australia won by nine wickets on Tuesday to level the series at one-all.
"Jason has undertaken a thorough rehabilitation program since suffering the injury in Adelaide and his progress is certainly encouraging," Australia team physiotherapist Errol Alcott said in a statement.
"He has bowled off a full run a number of times now, and despite not showing any signs of pain, he will remain under daily review up until the Sydney Test."
Squad: Steve Waugh (captain), Justin Langer, Matthew Hayden, Ricky Ponting, Damien Martyn, Simon Katich, Adam Gilchrist, Andy Bichel, Brett Lee, Jason Gillespie, Stuart MacGill, Brad Williams, Nathan Bracken
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