Australian all-rounder Cameron Green remains an "outside chance" to play the first Test against India despite lingering injury troubles, coach Andrew McDonald said Saturday.

Green has been sidelined since the end of last year when a sharp delivery from South Africa's Anrich Nortje fractured his finger in Perth and forced him to miss the final Test of that tour.

The 23-year-old was named in Australia's squad in the hopes he would be match fit for the four-Test series starting Thursday in Nagpur.

"We've got a fair bit to work through before the first Test match, but we haven't put a clear line through him or... put him on the team sheet yet," McDonald told reporters in Bangalore after a morning training session.

"He's made some significant steps forward in the last couple of days, probably to my surprise," he added.

"So there's still an outside chance that everything going well he might be on the team sheet."

The series is Australia's last before this year's Indian Premier League season gets underway.

Green became the T20 league's second-most expensive overseas player ever in December when he was purchased at auction by the Mumbai Indians.

Australia are in the middle of a four-day warm-up regime in Bangalore before they head to Nagpur next week.

India hold the Border-Gavaskar trophy after triumphing in their last three series against the Aussies, who last won a series in India back in 2004.

Australian skipper Pat Cummins expects a hard slog leading the tourists' pace attack but said he was excited for the looming showdown between the world's top two Test teams.

"Coming here to India, a lot of the talk is around big spinning wickets, maybe fast Test matches, but it's not always the case," he told reporters.

"You need to get into the grind at times," he added. "That role as a fast bowler may be just bowling plenty of overs for not a heap of reward, but doing your job for the team.

"I really enjoyed that aspect of the last tour. There's always plenty of people watching, so lots to play for."