On Thursday, the newspaper, Al-Seyassah, quoted Sisi as saying in an interview that he had no alternative but to meet the wishes of the Egyptian people for him to run.
"I will not reject the demand," said Sisi, who is seen as a decisive figure that can ease political turmoil that has hit Egypt's economy hard.
"I will present this to the Egyptian people to renew confidence through free voting."
There was no official confirmation that Sisi will contest elections expected within six months.
Deposed president Mohamed Morsi and his Muslim Brotherhood movement accuse Sisi of staging a coup and undermining democratic gains made since a popular uprising ousted autocrat Hosni Mubarak in 2011.
After deposing Mursi, Sisi unveiled a political roadmap meant to lead to free and fair elections.
But under his watch, security forces have mounted one of the fiercest crackdowns against the Brotherhood and stifled dissent, drawing fire from human rights groups.
About 1,000 Brotherhood members have been killed in the streets, top leaders have been jailed and the group has been declared a terrorist organization.
The Brotherhood, which says it is a peaceful organization, has been largely driven underground. But it is resilient and is likely to keep challenging Sisi.
Sisi has become deeply popular in Egypt. There are Sisi posters, T-shirts and even chocolate bars. He is portrayed as a savior on state and private television channels.
But Sisi is aware that Egyptians, with the help of the army, ousted two presidents in three years. If he doesn't deliver, mass protests could erupt again.
"We will not play with people's dreams or tell them we have a magic wand," said Sisi in the interview with the Kuwaiti newspaper. "I will tell them let's join hands and work together to build this country of 90 million."
On July 3, Egypt’s Army announced that president Morsi was no longer in power. They also dissolved the Egyptian constitution. The Chief Justice of Egypt’s Supreme Constitutional Court, Adli Mansour, was sworn in as interim president on July 4.
NTJ/NJF