One of the most engaging political questions in Egypt today is whether General Abdel Fattah al-Sisi, who ousted the country's first democratically elected president, will run for the job himself.

But Egypt's new strongman, hugely popular among the large segment of the population that called for Islamist president Mohamed Morsi to be removed, is keeping mum.

For now, Egypt is still undecided on the shape that its future governmental structure will take, be it presidential, parliamentary or semi-presidential.

Interim president Adly Mansour has formed a panel to draft a new constitution, replacing one rammed through by Morsi that was criticised for being too Islamist in nature.

In principle, the talk is of elections -- both for a new parliament and the presidency -- sometime in the middle of next year.

Meanwhile, the local media is full of speculation about a possible Sisi candidacy.

On July 3, Sisi appeared on state television and declared that Morsi had been pushed out.

He said he acted after millions took to the streets demanding the removal of the Islamist leader -- the first civilian and first democratically elected person ever to hold the presidency -- who had been in office for only a year.

His portrait is everywhere

Since then, calls for Sisi to run have proliferated on Facebook pages. Portraits of the strongman are ubiquitous in shop windows, on walls and in cars in the Arab world's most populous country.

Experts and journalists who have recently met Sisi say he does not want the top job and has no intention of running for it.

And the man himself has made only one public pronouncement on the matter, and that was enigmatic.

In a speech on July 24, three weeks after ousting Morsi, he said "the honour of achieving a popular demand is bigger than the honour of leading Egypt".

Regardless of what he decides, Egypt faces a dilemma, as the military has always played a prominent role in politics.

At the same time, it is grappling with two serious security issues.

First, there are fears that an Islamist insurgency may be emerging in response to the army's ruthless crackdown on the Muslim Brotherhood over the past several weeks.

And secondly, the army is dealing with growing lawlessness in the Sinai Peninsula that has seen repeated deadly attacks on police and military installations.

Abdullah al-Sennawi, an editorialist at independent Al-Shoruk daily, said: "He stands or not, in both the cases we are faced with a problem."

"It is clear that he has strong support from the army, security services and state apparatus. That makes him powerful. So if somebody else is elected, we risk having two heads of state."

At the same time, "forces such as the Muslim Brotherhood would make it difficult for the future president," he said.

"As a result, (the next president) will have to depend on the military, which will weaken the executive. So the issue goes beyond Sisi."

Political analyst Mustafa Kamel el-Sayyed said the military chief and the executive head must "coexist".

Given the reality in Egypt, the "next president will have no influence on the army".

"It is realistic to think that the army would continue to play a role, especially under Sisi," Sayyed said.

Since the 2011 ouster of Hosni Mubarak, Egypt has been plagued by instability, which has grown since the coup.

For some experts it is precisely this concern that makes a case for Sisi to stick with one job -- heading the military.

'Sacred duties' as army chief

Ahmed Taha, a writer for private daily Al-Youm al-Sabaa, addressed himself to everyone wanting to convince Sisi to run.

"I urge them to leave him to his sacred duties" as the head of the army.

That is "more important than being head of state, as internal and external dangers to the nation require the army's capacities to be reinforced, and only Sisi can" do that, he said.

Sennawi told AFP Sisi even said he "would not run for presidency even if millions" of supporters took to the streets.

But if he did, the three men who lost out to Morsi in last year's presidential election said they would support him.

Amr Mussa was a long-time foreign minister under Mubarak and then head of the Arab League.

"Today, the Egyptians expect their future president to take firm decisions, whatever the political implications," he said in an interview with Al-Shoruk, adding that "General Sisi is at this moment the most popular man in Egypt".

Ahmed Shafiq, briefly prime minister during Mubarak's last days in power and the loser to Morsi in a run-off, told private television channel Dream 2 that the general gets "absolute priority" if he decides to run.

And Hamdeen Sabbahi, an Arab nationalist, has called Sisi a "popular hero".