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A call on the captaincy of Australia’s T20 team is also likely to follow soon, with Finch revealing last weekend he would consider his future in that format after this summer.
Cummins, Warner, Steve Smith and Alex Carey remain the likely front-runners to fill the roles between them, as a mix of the new and old of Australia’s leadership brigade.
Cummins himself would likely be the preferred option as Test skipper, but the fact the quick has missed 28 of the past 66 ODIs makes that decision far trickier.
After initially claiming he did not want to juggle all three roles when he took over the Test team last summer, Cummins signalled his interest on Tuesday with some caveats.
“I think if you were going to do all the formats and every game, I don’t think that’s realistic,” Cummins told reporters at Kayo’s cricket launch.
“Especially as a fast bowler I think you do need to find windows to rest. But I think you can manage that as well.
“It’s not something I have really thought about.
“I am really happy with captaining the Test side … I don’t think they need to rush into any decision.”
Cummins’ suggestion would likely include something along the lines of co-captains, something not pursued in Australian cricket so far.
Meanwhile, Cummins also backed Warner’s leadership capabilities, pointing out that the opening bat had assisted in making the start to Test captain easier in the past year.
Warner remains banned from leading any Australian team following the 2018 ball-tampering scandal, but stated on Tuesday he would be “privileged” to lead Australia’s one-day team.
Cricket Australia chair Lachlan Henderson has also indicated he would like the board to meet with Warner, with the 35-year-old having long been keen to speak with officials about lifting the ban.
“Obviously (Pat) is the key (on whether he wants lead the ODI team), he is the Test captain and gets the first opportunity,” Warner said.
“But any opportunity you get asked to captain, it’s a privilege.
“For my circumstances that’s in Cricket Australia’s hands. I can only concentrate on what I have to do, and that’s using the bat and scoring as many runs as I can.
“My phone is here (if CA want to talk). At the end of the day what is done is done in the past.
“The good thing is there is a new board. I am always happy to sit down and have a chat and talk about whatever they need to talk about.”