Greste and Canadian-Egyptian Mohamed Fahmy were sentenced in June to seven years in jail, and Egyptian Baher Mohamed for 10 years for defaming Egypt and aiding banned Islamists.
All three remain in custody pending a new hearing, Egypt's top court ruled yesterday.
Greste's brothers Mike and Andrew said the decision by the Court of Cassation was a "positive step in the legal process and one step closer to justice being served".
"Following instruction from Peter and the family, Peter's Egyptian lawyer lodged an application with the Egyptian attorney-general's office to have Peter deported pursuant to a presidential decree that was issued in November," the brothers told reporters in Brisbane, adding that the application had been made several weeks ago.
"Now that Peter is an accused person, we will be making an amendment to this application seeking his deportation."
"We just see the next couple of days as a pivotal point in the case and a perfect opportunity for the (Australian and Egyptian) governments to exchange information and views and hopefully come to a decision on a deportation," he said.
Australian Foreign Minister Julie Bishop said Greste could be transferred back to Australia under the decree, although it had yet to be tested.
"The law is not very clear. It is a new law. But it does provide for a couple of options for prisoners to be transferred back to their home country -- in this case, Australia," Bishop told the Australian Broadcasting Corporation.
If the deportation application fails, the brothers said Greste's lawyer would apply for bail at the retrial, adding they had been advised that it could start in 45 days.
The three defendants were not at the hearing in Cairo, which lasted just 30 minutes.
Hopes for their release have grown since a thaw in diplomatic relations between Egypt and Qatar, where Al-Jazeera is based.
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