The pace bowler has secured 309 wickets in 71 appearances with an average of 22.10.
Australia's chair of selectors Bailey has stated that pace spearhead Cummins will play a "major part" in this winter's Ashes series.
Rumors had circulated that the veteran bowler might sit out due to a persistent back stress problem that remained unresolved.
Earlier indications from the squad suggested no final decision had been made regarding Cummins' participation, with the five-Test series scheduled to begin on the 21st of November in Western Australia.
He revealed that his recovery is on track and remained hopeful about the likelihood of participating.
"It's clear that the clock is ticking and there are permutations at play, not just the physical problem, but other factors as well," the selector added.
"We're encouraged. There's strong faith that he will feature a key capacity. Hopefully it's the first Test. If not, we'll reassess."
Past Concerns
Cummins was ruled out the ODI and T20 games against India and New Zealand in the previous weeks after examinations confirmed a lumbar bone stress.
There is a track record of recurring issues, with setbacks in 2012-13, 2013-14 and 2015-16 leading to absences from several home seasons in a limited period.
Cummins stated he would be ""aggressive" and "take risks" in his rehabilitation process to secure his spot for the series.
He mentioned that there was no confirmation if Cummins had begun bowling as part of his comeback but conceded it was "becoming urgent" for him to recover fully for the first Test.
Backup Options
Should Cummins not be fit, veteran batsman Smith will take over the captaincy.
The talented all-rounder was withdrawn recently from Australia's squad for their one-day international series against India as a safety move because of discomfort in his torso.
Bailey described it as a "small issue and stated that Green will play in the Sheffield Shield, so will be "ideally positioned to deliver overs."
"Extensive planning has gone into developing the strategy for him to participate for the opening match as an dual-role player," Bailey explained.
"His involvement was limited to the initial matches anyway. The way he swings the willow in shorter formats, if it causes any delay for another day, we opted to approach this more conservatively."
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