The bans on Steve Smith, David Warner and Cameron Bancroft could be reduced by Cricket Australia (CA).
Smith and Warner were suspended for 12 months and Bancroft for nine for ball-tampering in South Africa in March.
An independent review commissioned by CA found the body to be "arrogant and controlling" and partly to blame.
According to its news website, the CA board will discuss the situation in a phone call early this week.
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Smith, captain at the time, and Warner, his vice-captain, are eight months into one-year bans, while Bancroft, who carried out the cheating in South Africa, will be eligible to return in December.
"These contrite men have suffered enough. Let them play," said Greg Dyer, head of the players' union, in October.
Australia have struggled since the trio were banned. They lost a one-day series in England 5-0, a two-match Test series against Pakistan 1-0 and were beaten 3-0 by the same opponents in a T20 contest.
They have also lost a one-day series against South Africa 2-1 and host India across all formats of the game this winter on home soil, starting with a Twenty20 match in Brisbane on Wednesday.