Sisi, who has a large and loyal following in the country, said he would run "at the request of the people." Several draft movements including one dubbed "By Command of the People" have encouraged the general, who also serves as the country's defense minister, to run.
Sisi and the military ordered Morsi's Islamist regime, elected after the deposition of former dictator Hosni Mubarak in 2011, out of office after mass street protests against his government.
"If I run for presidency, it would be by the request of the people and by a mandate from my army, as we work within a democracy," Sisi said in a speech Saturday.
Egyptians are set to vote on a new constitution next week, a document drafted after Morsi's ouster. His supporters have pledged to boycott all future elections after the military coup.