Starc has missed Australia's previous two Tests after suffering the frustrating injury to his left finger while fielding off his own bowling against South Africa in December.
The 33-year-old was sorely missed in Nagpur last week as India smashed Australia by an innings and 132 runs to open the Border-Gavaskar series with a commanding win.
The tall left-armer stayed back in Sydney to recover, only arriving in India on Saturday, and joining up with his teammates in Delhi on Tuesday night ahead of the second Test starting on Friday.
Captain Pat Cummins and Victorian quick Scott Boland were Australia's only fast bowlers in Nagpur, as allrounder Cameron Green (broken finger) missed, and new spin sensation Todd Murphy partnered veteran Nathan Lyon as the team's slow bowlers.
"I'd like to be a little further down the road," Starc said in Delhi on Wednesday.
"Still a good chance so it'll come down to how it reacts by the end of (Wednesday), how the medical staff see it, how the selectors and Pat (Cummins) and Ronnie (coach Andrew McDonald) feel about it as well.
"I'll do everything I can to be fully available for selection, then it's a discussion for the rest of the group involved."
Starc said he planned to bowl "as normal" but admitted he was struggling to get the finger back to full strength.
"I don't think (batting will be an issue) so it's going to be uncomfortable but I don't think it's an issue," he said.
"I think I'll still field with a cap on (the finger), that's what I did in Melbourne (after he initially broke the finger)...I don't field myself in slip anyway."
Australia are also weighing up whether to rush Green back into the XI, which would give the tourists the opportunity to play a third spinner - Matt Kuhnemann.
It was initially feared Green would be fit to bat before he could bowl, but he was having more trouble with the latter during Wednesday's training session.
The 23-year-old looked at near-top pace when he bowled on a centre wicket pitch, but looked decidedly shakier when it came time to bat in the nets.
Australia landed in the Indian capital knowing they need to win, or at the very least - draw - to keep the blockbuster series alive.
Australia are confident they can bounce back in the spin-friendly conditions, despite never having won a four-Test series after going down 1-0.
India have not lost a Test at Delhi's Arun Jaitley Stadium since 1987.
"Obviously a challenge of a week but we move onto the second Test and it presents a new challenge," Starc said.
"I'm not sure we'll see conditions change too much from last week with how the guys have discussed it.
"I think judging on the last couple of days the wickets out the back are similar in many ways to what the centre is."
Australia boldly dropped Travis Head, the world's No.4 batter, for the first Test based on his poor record in Asia.
Peter Handscomb, in his first Test since 2019, performed serviceably at No.6, but Matt Renshaw had a nightmare match with scores of 0 and 2 batting in Head's usual position.
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