Andrew McGlashan is a deputy editor at ESPNcricinfo
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When Finch was ruled out of the second T20I in Sydney, Matthew Wade stepped up to captain Australia for the first time, in the absence of vice-captain Pat Cummins, with coach Justin Langer saying there was "a process" that needed to be gone through before Smith could lead again following his loss of the captaincy after the ball-tampering scandal in 2018.
"There were discussions sort of taking place," Smith said. "I think JL [Langer] answered the question when asked about me and captaincy and stuff. There's obviously a process that needs to be done. For me I just said I'm happy to do whatever is best for the team and that's the same going forward.
"Right now Tim and Finchy are doing really good jobs in both the formats of the game. I'm comfortable where I'm at right now but as I've always said I'll do what's best for the team.
"I think whenever there is a captain chosen, I think you go through a process where you go to the board and things like that, so I'm sure it won't be too dissimilar. It's probably more of a question for someone a bit higher up. That's all that has been said to me and, yeah, we'll let it rest for now."
One of the challenges Australia could face when replacements for Finch and Paine are eventually needed is the relative lack of captaincy experience among possible replacements other than Smith.
Current vice-captain Cummins has not had any chance to captain at state level and would be unlikely to get it given the limited number of games he plays for New South Wales. Marnus Labuschagne, who has been touted as another option, also has yet to have any captaincy experience.
Travis Head, who recently lost the joint vice-captaincy position, leads South Australia and captained Australia A in the recent tour match against the Indians. Alex Carey will lead the side in the second match at the SCG starting on Friday.