Cameron Green thinks he and Mitchell Starc will be "touch and go" to be fit for the start of a four-match Test series against India.

Green underwent surgery after breaking his right index finger during a victory over South Africa in the Boxing Day Test at the MCG.

Starc damaged his middle finger in the same match in Melbourne, with both players missing out as Australia attempt to secure a 3-0 whitewash of the Proteas at the SCG.

Australia start the first Test against India in Nagpur on February 9 and Green believes that contest could come too soon for himself and paceman Starc.

He told SEN WA: "I think me and Starcy are maybe touch and go for that first one but obviously we'll give ourselves the best chance.

"[It's] going well. Had successful surgery in Sydney and the surgeon is really happy with how it went. I think he did Tim Paine's successful surgery, so it fills me with a lot of confidence.

"The rehab is having two weeks of time [off], then two weeks to start running and get the shoulder and back moving just to double-check they haven't frozen over. Then probably at the four-week mark I'll try and hold a ball and see how that works.

"Try and hold a cricket bat and see how it feels. At the moment [the finger] feels really good, pain-free, so that gives me a bit of confidence in four weeks' time that it will be all good.

"We meet over in Sydney for the Allan Border Medal [ceremony], then we leave the next day to go to India."

Starc also dismissed talk that he may not be able to bowl for the Mumbai Indians at the start of his first Indian Premier League campaign.

He said: "No, that's not correct. I've heard about this for quite a while now. I don't know where it's come from. We've spoken to the selectors. I've heard that I'm 100 per cent available for both skill sets in the IPL at the start, so I'm not too sure where that's come from.

"Obviously my first priority is the Test series that's beforehand, getting myself right for the first Test."