Cummins is recovering from a back stress injury and has yet to resume bowling, leaving him racing against time to be fit for the opener, which begins on November 21. The 32-year-old admitted on Monday that he is unlikely to feature in the opener and remains uncertain for the second test in Brisbane.
Australia coach Andrew McDonald had previously said Cummins would need to start bowling at least four weeks before the Perth test to avoid risking further injury.
"It's progressing. He's building up. He's optimistic about it," Bailey told reporters on Saturday. "I think actually the more he's done over the last few days, the more optimistic he's become but I categorically don't know if he's bowled a ball.
"We know time is getting short and there's permutations around that, not just around the back, but other factors as well. It's positive. (We are) really confident that he's going to play a major part.
"Hopefully it's the first test. If not, then we'll pick it up."
In another setback for Australia, all-rounder Cameron Green was ruled out of the One-Day International series against India due to "low-grade side soreness" sustained in training.
Australia added Green would likely return to play in Shield cricket, while Bailey eased concerns about a serious injury to the 26-year-old.
"It is minor and it's conservative, and I think this decision probably ensures that we do have enough time to make sure," Bailey said.
"We put so much time and energy into building out the plan for him to be available for the first Test as an all-rounder.
"So for the sake of, he was only going to play the first two ODIs anyway."