Mr Abbott is due in New York tonight for the General Assembly meeting and it would offer a rare chance for a face-to-face meeting with the Egyptian leader on the sidelines.
Al-Jazeera journalist Peter Greste was sentenced to seven years jail in June for providing supporting to the banned Muslim Brotherhood.
His trial along with two colleagues is widely seen as a politically motivated case against the Qatari government, that supports the Brotherhood and also finances Al-Jazeera.
“I would like to think there is an opportunity to meet and remind President el-Sissi that while this matter, this case goes on, that Australian-Egyptian relationships can never be the same as they were before December,” said Juris Greste after returning from 10 week visit to Egypt to see his son in jail.
“I would also like to say I hope he (Mr Abbott) can ask that this be speeded up... and that the judicial system, is not delayed,” said mother Lois Greste.
Mr Abbott's office said he hopes to meet with President el-Sissi at the UN.
The family of Egyptian-Canadian journalist Mohamed Fahmy have asked the Canadian prime minister Stephen Harper to raise the case with Mr el-Sissi at the UN.
Peter Greste was arrested last December along with Al-Jazeera English colleagues Baher Mohamed and Mr Fahmy.
All three protested their innocence and the way their trial was conducted.
No date has been set for Peter Greste’s appeal.
The Egyptian president last week said he would not intervene in the legal process but refused to rule out a pardon afterwards.
Peter Greste's parents said he is keeping his spirits up in jail with calligraphy and he has started studying a masters degree in international relations.
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