Greste and Canadian-Egyptian Mohamed Fahmy were sentenced to seven years in jail, and Egyptian Baher Mohamed for 10 years, for defaming Egypt and aiding banned Islamists in a case which sparked international uproar.
All three remain in custody pending a new hearing, which analysts said could be a step towards the release of the journalists after more than a year in prison.
Australia and the US have led calls for the three to be released, but hopes have grown as diplomatic relations have thawed between Egypt and Qatar, where Al-Jazeera is based.
Greste’s brothers Mike and Andrew said the decision by Egypt’s Court of Cassation on Thursday was a “positive step in the legal process and one step closer to justice being served”.
But they added that a decree from Egyptian President Abdel Fattah al-Sisi in November allowing him to deport foreigners sentenced to prison or on trial was “the best option to get Peter home”.
“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 was made several weeks ago.
“Now that Peter is an accused person, we will be making an amendment to this application seeking his deportation.”
Hundreds of journalists and supporters, many with black tape over their mouths, held silent protests after the three journalists were sentenced to challenge what they see as growing media censorship in Egypt.
Egyptian authorities have been incensed by Al-Jazeera’s coverage of their deadly crackdown on supporters of ousted president Mohamed Morsi, accusing Doha of backing his Muslim Brotherhood party after Morsi was deposed in July 2013.
The Brotherhood, which saw electoral success after the overthrow of longtime strongman Hosni Mubarak in 2011, has since been declared a “terrorist organisation” in Egypt.
Andrew Greste said the family hoped a decision would be reached within the next few days, but that they did not expect to speak to Peter until Sunday.
“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.
Mohamed’s wife Jihan welcomed the retrial as a “small but positive step towards my husband being freed”.
“This past year has been the worst year of my and my children’s lives,” she added.
Fahmy’s fiancee Marwa Omara said before Thursday’s ruling that a request had been filed to deport him to Canada if a retrial was ordered.
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.
“As I understand it, the law would operate such that he would come back to Australia to face legal proceedings in Australia.”
Andrew Greste said the lack of a precedent for the decree meant his brother’s legal situation was in “uncharted waters”, but added: “I would like to think that the decree was enacted for a reason to be used.”
If the deportation application fails, the brothers said Greste’s lawyer would apply for bail at the retrial, which they had been advised could start in 45 days. (AFP)