Egypt's army has been holding talks with government and protest leaders, as the deadline it set for a resolution to the mass protests approaches.
President Morsi has rejected an ultimatum to "meet the demands of the people" or face military intervention.
He says he is Egypt's legitimate leader and will not be forced to resign.
The army says it will issue a statement after the 16:30 (14:30 GMT) deadline expires, and now has control of the state TV building.
Clashes broke out at rival protests across the country overnight, with at least 16 pro-Morsi protesters killed at a demonstration at Cairo University.
His opponents say he and the Muslim Brotherhood party from which he comes are pushing an Islamist agenda onto Egypt, and that he should stand down.
The Brotherhood has said the army's action amounts to a coup.
In a defiant televised speech on Tuesday evening, Mr Morsi said he would give his life to defend constitutional legitimacy, and blamed the unrest on corruption and remnants of the ousted regime of Hosni Mubarak.
In a statement on Tuesday , the army swore to "sacrifice even our blood for Egypt and its people, to defend them against any terrorist, radical or fool".
The army's plan reportedly includes an outline for new presidential elections, the suspension of the new constitution and the dissolution of parliament.
However one military source told Reuters news agency that the deadline would mark only the beginning of talks.
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At the scene
BBC News, Cairo
Some are busily going about their normal day today, others will be protesting again - but many will be holding their breath.
Some of the headlines in the morning papers reflect the overwhelming mood here, with bold lines like "The collapse of the Brotherhood" and "The return of Egypt in a few hours". Others wonder what will happen next: "Army Deadline Ticking Down as Hopes Dim for Way Out" says the Egyptian Gazette.
President Morsi, the wider Muslim Brotherhood and their supporters are up against two formidable opponents - the wider public still taking to the streets in large numbers and the army.
The military's deadline is fast approaching. How the army handles this is key to how it will all play out as both sides dig in their heels with no signs of a compromise on the horizon.
On Wednesday, a defence ministry official said army chief Gen Abdel Fattah al-Sisi was meeting his top commanders as the deadline approached.
A source close to the military told AFP news agency they were discussing details of a post-Morsi roadmap.
Members of the Tamarod (Rebel) movement, which has mobilised millions of demonstrators onto the streets to demand Mr Morsi's resignation, were also part of the talks.
Also at the meeting were leading religious figures and opposition leader Mohammed ElBaradei. An opposition source told Reuters Mr ElBaradei would "urge the armed forces to intervene to stop the bloodshed".
But a spokesman for Mr Morsi's Muslim Brotherhood party said the army had no right to offer such a plan.
"A roadmap is something that the constitution outlines and the president directs. It's not the role of the military," said Gehad el-Haddad.
He said the Brotherhood was open to any solution, but that it had to be through "representatives of the people", and proposed speeding through parliamentary elections.
"If the protests on the street prove anything they prove the people of Egypt are ready to have their say. They can sweep the parliamentary election, impeach the president, change the constitution and set the roadmap that they want, but it has to be the right of the people."
Military sources earlier told the BBC the president's position was becoming "weaker" with every passing minute and suggested that, under the draft plan, he could be replaced by a council of cross-party civilians and technocrats ahead of new elections.
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The president was put under further pressure by the resignation of six ministers from his government on Monday, including Foreign Minister Kamel Amr.
Mr Morsi became Egypt's first Islamist president on 30 June 2012, after winning an election considered free and fair following the 2011 revolution that toppled Mubarak.
But dissent has been growing, with protesters angry at the lack of change in post-revolution Egypt and accusing the Brotherhood of trying to protect its own interests.
"This is a president threatening his own people. We don't consider him the president of Egypt," said Mohammed Abdelaziz, a leader of Tamarod.
However, Mr Morsi and the Brotherhood still have significant public support, and both sides have drawn huge numbers to rallies in recent days.
Thousands gathered in Tahrir Square in central Cairo on Tuesday afternoon to demand Mr Morsi step down. There were outbreaks of violence in several parts of the capital, with casualties reported at hospitals in the north, south and centre of Cairo.
In the largest bout of unrest, at least 16 people were killed and about 200 wounded at Cairo University in Giza. Eyewitness Mostafa Abdelnasser told AFP that Morsi supporters had come under attack from unidentified men carrying firearms.
Clashes were also reported in Alexandria, Egypt's second city, on Tuesday.
Crowds began gathering in Tahrir Square again on Wednesday morning, with numbers expected to rise throughout the day.
On Monday, eight people died as activists stormed and ransacked the Muslim Brotherhood's Cairo headquarters.
In the wake of the latest unrest, the UK Foreign Office has changed its travel advice for Egypt, recommending against all but essential travel to the country except for resorts on the Red Sea in South Sinai and in the Red Sea governorate.
The instability has also hit global oil prices, sending US light crude above $100 a barrel for the first time since September last year, amid concerns supply routes through the Suez Canal could be affected.