President Abdel Fattah el-Sisi, who rose to power after overthrowing Mohamed Morsi, an Islamist president, in 2013, has yet to announce his candidacy, but he is expected to run, and critics worry that he will try to exclude any real competitors.

Two other candidates who have entered the race are currently facing charges that many believe are politically motivated. If they are convicted, they will be ineligible to run.

Since returning to Cairo from the United Arab Emirates a few weeks ago, Mr. Shafik has spent most of his time in a suite at a luxury hotel in Cairo, declining to give interviews while Egyptian politicians and ordinary people wondered whether he was under arrest. His relatives and aides said that he was not allowed to speak to anyone nor go anywhere without the permission of Egypt’s security agencies.

Even though he prospered in the era of Hosni Mubarak, who was ousted from power in 2011 by a popular uprising, Mr. Shafik has a large base of supporters in Egypt. His military record, and name recognition, may have made him a strong candidate.

He fought in Egypt’s two wars with Israel, in 1967 and 1973, and rose to command the Air Force. As minister of civil aviation, a post he held for a decade beginning in 2001, he oversaw the modernization and development of the national airline and the Cairo airport.

In a bid to bolster his support during his last days in power in 2011, Mr. Mubarak promoted Mr. Shafik to prime minister in the hope that he could resolve the crisis brought about by a popular uprising.

Mr. Shafik lost the presidential election to Mr. Morsi the next year by only about 2 percent of the vote.