Australia allrounder Cameron Green is racing the clock to be fit for the first Test in India as he recovers from a broken finger.

The towering Western Australian had surgery after being injured in the Boxing Day Test against South Africa.

The incident to Green's finger happened just a day after his first five-wicket haul, continuing his rapid improvement at Test level.

The 23-year-old has been involved in Australia's training camp in Sydney but the first match of the blockbuster four-Test series against India is only 11 days away, begins in Nagpur on February 9.

Australia coach Andrew McDonald said Green could be played as a batter only if he was still unable to bowl.

However, it is likely a specialist batter like Matt Renshaw or Peter Handscomb, who have red-ball experience in India, would be preferred at No.6.

"Where he's (Green) positioned at the moment, his biggest challenge is bowling," McDonald told reporters on Sunday.

"There is a lack of loading there, and one of the key reasons around us getting into this camp early is to make sure that we're ready to go for the rigours of what the bowling unit (is) going to encompass.

"Building confidence is the main thing, setting him up to succeed if he was to play in that first Test match, having enough time, that will be the critical question.

"We value his batting first and foremost really. He's a batter in our top six and we value that. His bowling is a very nice bonus."

Star quick Mitchell Starc, who also suffered a finger injury in the last Test of 2022, has already been ruled out of the first match of the Border-Gavaskar Trophy.

The tall left-armer will not leave with the rest of the squad when they depart Australia this week but is making solid progress in his recovery.

McDonald remains hopeful Starc will be available for the second Test in Delhi, starting on February 17.

"It's probably frustrating for Mitch that he feels that good," McDonald said.

"But the good thing is when he does get out of the splint all his workloads are going to be up to speed and it will be pretty much into that second Test, which is good news to us."

Meanwhile, McDonald was unperturbed by veteran opener David Warner's claims of "exhaustion" ahead of the expected gruelling tour of India.

"It's been a long Test summer," McDonald said.

"He's had some off-field issues that's played out and taken some strain, some mental energy away from him.

"He's put some time into the Big Bash, and I think he's done a fantastic job.

"Our challenge will be to manage him into that first Test match, no different to any other series where you'll have players come in at different stages in term of fatigue."