Finch did some running on Wednesday and would test his hamstring again at training on Thursday before deciding if he will play.
"I'm maybe 70-30," Finch said prior to training on Thursday. "But I'll test it out properly this afternoon to make sure that I'm not hindering the side at all leading into the game. That's the worst possible scenario, that you leave the guys short out there with one player fewer."
Finch, having already retired from ODI cricket and hinted at this tournament being his last in T20I cricket, was adamant that sentiment would play no part in his decision-making.
"It won't make it harder one bit," Finch said. "If I feel like it 1% would be compromising the side's performance I won't play.
"If I don't feel confident in my hamstring, then I won't play and that might be in the first effort that I do today, it might be in the last one. If I feel any pain or anything like that I won't play."
Finch confirmed that David would face the same fitness test on his hamstring at training.
"I think the scan results showed a very similar thing," Finch said. "He's in exactly the same boat, he'll get worked out today.
"I'm maybe 70-30. But I'll test it out properly this afternoon to make sure that I'm not hindering the side at all leading into the game."
Aaron Finch
"We'll know more during training, the likelihood of both of us playing, one of us playing, neither of us, whatever that looks like, it's exactly the same. You don't want to compromise the team's performance by having a guy go down who comes in with a niggle. That will be one of the things we go through as well and make sure it's all ticked off this afternoon."
Finch said there were a number of different combinations Australia could go with depending on whether he and David were fit and would not speculate on the options. He also said Australia have not discussed the net run rate equation.
"Not as a team we haven't," Finch said. "I've talked a little bit with the coach. We went through it this morning briefly. Like I said last game, you still have to earn the right to push for a net run rate, because the last thing that you want to happen is you push too hard, you compromise the two points, and then potentially something happens in the Sri Lanka-England game and you leave yourselves vulnerable. But there are some scenarios that we need to keep an eye on throughout the game that if we get in a good position we can maximise that."