The Al Jazeera journalist and his two colleagues, Mohamed Fahmy and Baher Mohamed, were imprisoned last year on charges of spreading false news and supporting the banned Muslim Brotherhood.

Greste was originally sentenced to seven years jail and has spent 400 days behind bars.

Earlier this month Egypt's Court of Cassation ordered a retrial of Greste and his colleagues and at the time, his family said they were pinning hopes for their son's freedom on his chances of being deported before a second trial.

According to unconfirmed reports out of Egypt on Sunday, a presidential decree was issued in past few hours clearing the way for Greste to return home.

On Sunday morning, Greste's brother Andrew tweeted:

Until @PeterGreste butt is on a 747 outside of Egyptian airspace the campaign to free him continues. We've been let down before. — Andrew Greste (@AndyroosteG) January 31, 2015

I would welcome the news that@PeterGreste will be deported tomorrow. As yet I have no official confirmation. Rumours, rumours, rumours — Andrew Greste (@AndyroosteG) January 31, 2015

On Saturday, The Australian published a letter from Greste to mark his 400th day in prison.

"Despite all the talk, all the recognition of the injustice of our arrest, trial and conviction, all the diplomatic and political pressure, we are still in prison with an indeterminate stretch behind bars ahead of us," Greste said.

"Certainly, when we were arrested on December 29, 2013, none of us or our families seriously believed the ordeal would last this long. The absence of evidence that we had committed any crime was complete, and we were all convinced that common sense would prevail sooner rather than later.

"Very few Australians would understand what it's like to be innocent but still spend 400 days in a Middle Eastern prison. It is incredibly emotionally draining and infuriating. My primary hope is that one day something good comes of this."

A spokeswoman for Greste, Heidi Ross, said they had not heard anything and as it is the middle of the night in Egypt it was unlikely they would hear anything for several hours.

She also cautioned that rumours of Greste's release had occurred before.

"We've been here before".

Australian government officials are understood to be hopeful that there is substance to the rumours, but are being cautious.

Andrew Greste told ABC News 24 he had not heard anything about his brother's possible release other than what is circulating on social media.

"From our point of view and until we get official confirmation and as I said until his backside's on a plane outside of Egyptian air space on the way home it's business as usual from our point of view," he said.

Asked if he expected the Greste family would be given advance notice of his release or deportation, Andrew said: "As we've learnt in this whole episode we're in uncharted waters and a lot of these things are just unknowns.

"Our expectation is though or we hope that if he does receive a pardon then it could be at very short notice and literally hours that we're told that he's on the way."

He said an application for Peter's deportation has been before Egyptian authorities since early December. The application is supported by Australian consular officials.

"We'd welcome any form of his release, whether it be a pardon or deportation, we just want to get him home."

Andrew said his brother Michael is in Cairo and is constant contact with consular officials.

The rumours started after former Egyptian politician and now television talk show host Mostafa Bakry tweeted early Sunday morning, Australia time, from his @BakryMP account in Arabic: "I learned of a decision by the republic [ie. Egypt] to be published shortly that confirms the deportation of the Australian journalist 'Peter' who was convicted in the earlier case of the Marriott cell and al-Jazeera channel".

He then added: "The decision will be implemented tomorrow morning and he will be deported to his country of origin, Australia". 

Mr Bakry is well connected and close to President Sisi, but prone to outbursts. He previously said there was an American plot to assassinate President Sisi and threatened to kill Americans in retaliation.

Meanwhile, Australian authorities have today been quiet on the subject of Greste's potential release.

Former Victorian Premier Ted Bailleu, who ran a campaign to free the Al Jazeera journalist, said that "when Peter Gretes is released it will be very positive for Egypt, whenever that might be".