In his place Hilton Cartwright has managed to score just 1 run in both innings.
Australia physio Alex Kountouris put Finch through his paces with no sign of the calf injury slowing him down in an intensive sprint session.
His participation in the critical third encounter will only be confirmed on the morning of the match.
Opening partner David Warner told the press after training on Saturday morning: “It’s good signs to see him back in the nets and he’s doing everything possible to be fit for this game.
“We know what he’s going to bring. He’s a very good batter, he’s played a lot of cricket over the past couple of years, he’s got a lot of experience and for us at the top of the order, he brings a lot of aggression.”
Middle-order batsman Peter Handscomb was added to the squad as cover after Finch sustained the injury but didn’t play in the two losses.
Handscomb could slot into an out of sorts batting lineup with whom skipper Steve Smith is not pleased.
With keeper Matthew Wade struggling for form Handscomb could take the gloves while Cartwright is almost certain to be axed.
Warner defended Cartwright who has found opening a tough nut to crack saying: “It’s always challenging as a young guy to come into a team and take a bull by its horns.
“It’s very, very difficult.
“Especially when you come over here and play for the first time on the world stage against one of the best one-day teams in the world in their own park, it’s very difficult and it can be overwhelming.