Sisi, who toppled Egypt's first democratically elected President Mohammed Morsi last July, is believed to enjoy support within the army to stand in polls scheduled for later this year.
"If I nominate myself, there must be a popular demand, and a mandate from my army," Sisi was quoted as saying by the state-run newspaper Al-Ahram at a meeting with officials.
The audience broke into applause at his comments and chanted "we are all with you", the paper reported.
The army chief said the people should "assume their national responsibility of participating in force in the referendum in order to build a democratic and modern state that satisfies all Egyptians".
The referendum will be held on January 14 and 15 to replace the constitution suspended when Morsi was ousted.
Sisi has emerged as the most popular leader after the army overthrew Morsi, the Islamist leader of the Muslim Brotherhood, amid protests against his turbulent one-year rule.
Four persons were killed in fresh clashes across Egypt as pro-Morsi supporters began a march following Friday prayers yesterday.
One person was killed in Alexandria "when protesters fired at local residents," police official General Nasser El-Abd told the media in the coastal city.
Three others died in Suez after clashes broke out in El-Sabah city, where security forces fired teargas at a pro-Morsi march. Protesters responded by firing birdshot and fireworks, according to state news agency MENA.
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