Human rights groups condemned Ibrahim's conviction
After five hours of deliberation, the court's eight-judge panel said it would rule on 6 February on Saad Eddin Ibrahim's appeal.
It was the second time the panel had postponed a decision.
Ibrahim, 63, a sociology professor at the American
University in Cairo, was sentenced last May to seven years
in prison. The charges included tarnishing Egypt's image,
embezzlement and accepting foreign funding for his private
think-tank without government approval.
The court will also decide on 6 February on a request by Ibrahim's family for his immediate release from prison for health reasons. Ibrahim's wife has said her husband is suffering from an undiagnosed neurological disorder that requires urgent medical attention.
At the original trial, prosecutors focused on Ibrahim's writings about election fraud allegations and relations between Egypt's Muslim majority and its Christian minority, as well as his think-tank's voter education projects.
Mr Ibrahim was tried before a state security court, which means he has no right to a conventional appeal only to a review on technical grounds.
US concern
If the review request is granted, all 27 employees of Ibrahim's Ibn Khaldun research centre, who were convicted along with him, will get new trials.
In seeking a new trial, Ibrahim's lawyers have questioned the constitutionality of the law requiring private groups to get government permission to receive foreign funds, maintained the court did not fully consider the merits of the embezzlement charge, and said the defence team was not allowed to review all the evidence against the suspects.
Egyptian and international human rights groups have condemned the trial and conviction of Ibrahim and his staff.
Ibrahim holds joint US-Egyptian citizenship and his case has been repeatedly raised at the highest level by American officials.
But the Egyptian President, Hosni Mubarak, has refused to be drawn on the issue in public, saying it is a matter for the courts to decide.