Following the ball-tampering saga that rocked Australian cricket earlier this year, Australia have named Tim Paine as the skipper but are yet to name his deputy and Lyon, the country's most experienced Test player by some margin, is among the leading contenders to fill the role.
The 30-year-old was overlooked when Warner was appointed Smith's deputy in 2015 and while he has no senior captaincy experience, he is a highly respected member of the playing group.
Lyon says fellow bowlers Pat Cummins, Mitchell Starc and Josh Hazlewood are among those who need to take on extra responsibility, regardless of who gets the job.
"If they offered it to me, I wouldn't say no," Lyon told cricket.com.au.
"But it's not something I'm striving for. There will be a vice-captain appointed, but I think there'll be a good leadership group in that Test squad."
"Look at the bowlers, we've had some success together and gone through some hard times recently and that's only going to put us in good stead moving forward," he added.
Lyon is currently part of the touring Australia squad, that will take on England in a five-match ODI series from June 13.
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