Cummins said no decision had been made on the composition of Australia's XI as the selectors wait to see how Green and Starc recover later on Thursday.

"Starcy and Green had good sessions yesterday and we will assess them later on today," Cummins said on Thursday. "We don't have a line through them yet, we'll see."

Green is pivotal to Australia's side given he provides a genuine fifth bowling option and also opens the door for three spinners to play in Delhi.

Bowling is not an issue for Green but his batting and fielding remain a concern. He has not faced a fast bowler since he had surgery to repair his broken index finger after the Boxing Day Test. He batted for over an hour in the Arun Jaitley Stadium nets on Wednesday and faced throwdowns at full pace for the first time from Australia's batting coach Michael Di Venuto as well as a lot of spin bowlers.

Green also only caught hard cricket balls for the first time on Wednesday since breaking his finger on December 27 last year. They were also relatively gently-hit outfield catches before he returned to catching softer balls.

If Green plays, he will be well short of 100% and Cummins' conceded that it is a risk the selectors are carefully considering given his long-term importance to Australian cricket.

"Having a right-hander helps and him providing our fifth bowling option also helps," Cummins said. "He's a big player. It certainly helps the team function well from batting and bowling.

"You have got to be able to perform as well. He's still coming back from that injury. He's only had [one] session where he's catching with a hard ball. He had a really good session yesterday. We will see how he pulls up."

If Green is able to play, Cummins confirmed Australia are considering playing a third spinner in a five-man attack instead of Starc, even if Starc is passed fit to play.

"I think there's a conversation," Cummins said. "We'll work that out by the end of today, I hope.

"He's one of the world's premier bowlers in these types of conditions. We'll see. As I said, the wicket looks like it might turn a little bit. I thought last week with two pacers, that attack functioned quite well but I think whether it's Starcy, another spinner, Scott [Boland], variety in the attack does help."

Who will be the third spinner? Agar or Kuhnemann?

"We're open to both options," Cummins said. "We're really confident both will do a fantastic job out there. They both had long sessions the last couple of days and looked awesome. If we wanted a third spinner variety we'd be comfortable with either of those two."

Given Australia's horses-for-courses mentality, David Warner's record in India has been a topic of concern following his twin failures in Nagpur. Cummins did not explicitly confirm that he would play but he was confident he would be in the XI and would find a method to succeed after being pinned down by R Ashwin for 10 off 41 deliveries in the second innings in Nagpur.

"I'm not a selector. I don't think they've had a meeting but I'm sure Davey will be there," Cummins said. "You saw [last] year at the Boxing Day Test when he puts pressure back on the opposition, he's pretty hard to bowl to. You don't get as many good balls, so he knows that. I'm sure that'd be part of his plan. He has been batting really well here. Even in the lead-up, I thought he was fantastic. I know there's a lot of talk about spin bowling through the middle but with that new ball it's sometimes the hardest time to bat as well."

Cummins also revealed that Travis Head remains in the conversation to return to the side after he was sensationally dropped for the first Test in Nagpur due to his relatively poor record against spin bowling on the subcontinent. Head's value with the ball gives him a chance of a recall if Green doesn't play, as Australia did not get much out of their fifth bowling option in Marnus Labuschagne during the first Test. Cummins was full of praise for how Head had handled his omission.

"Trav has been awesome," Cummins said. "[He's] been working really hard out the back on his game. He's been fantastic around the squad like he always is. There's always plenty of fun wherever Heady is. He's absolutely part of the conversations for this Test, just like the first Test so he couldn't be doing any more. He's been fantastic."