Options likely to be discussed include cutbacks from Europe's €5 billion package of grants and loans promised last year, as well as a possible arms embargo against Egypt, said EU envoy to the South Mediterranean Bernardino Leon.
Egypt, the most populous Arab country, is enduring the bloodiest internal conflict in its modern history as the army, which deposed Mursi on 3 July after huge protests against him, cracks down on his Muslim Brotherhood party.
The upheaval is causing global jitters, but no consensus on how to respond has emerged in the West or the Arab world.
Leon said Europe still believed a political solution was possible in Egypt, where almost 900 people have been killed since last week.
"No options are being ruled out today," he said after a meeting of senior EU diplomats in Brussels, convened in reaction to the crackdown. "We are discussing responses to the current discussion in a very open-minded way."
Several foreign ministers have said in recent days that aid should be cut back, but on Monday many diplomats expressed concerns that withholding funds would likely hurt the Egyptian population more than the government.
European institutions have given no direct budget support to Cairo since 2012 because of a lack of democratic reforms. Most of the cash sent to Egypt goes to civil society.
Underlining the lack of global consensus, Saudi Foreign Minister Prince Saud al-Faisal on Monday pledged to fill any financial gaps left by Western countries withdrawing aid from Egypt.
Diplomats say EU governments are broadly divided between those who advocate taking a strong stance to support democratic principles in Egypt and others who say the bloc should preserve its impartiality and its ability to mediate in the future.
Britain's Foreign Secretary William Hague said on Monday that aid to Egypt should be reviewed without excluding future assistance.
"We have to stick to those principles ... of supporting institutions, not taking sides, of promoting dialogue and of keeping faith with the majority of people," he told BBC radio.
EU diplomats have said that the bloc could also use the possibility of suspending a broad cooperation deal with Egypt to pressure the government.
Dating back to 2001, the deal includes provisions for free trade in industrial goods and concessionary arrangements for trade in agricultural products.
Egyptian Foreign Minister Nabil Fahmy sought to pre-empt any attempt to use aid flows as a lever by saying he would look at all such assistance to see "what aid is being used to pressure Egypt and whether this aid has good intentions and credibility".
Mubarak to be freed?
An Egyptian court ruling has raised the prospect of freedom for deposed military strongman Hosni Mubarak.
The 85-year-old Mubarak, arrested after his overthrow in 2011, can no longer be held on a corruption charge, a court ruled on Monday in a decision his lawyer said removed one of the last obstacles to his release on bail. The ruling coincided with another decision from the public prosecutor to press new charges against Mursi of inciting violence.
A judicial source, without confirming that Mubarak would be released, said the former Egyptian president would spend at least two more weeks behind bars before the criminal court could make a final decision in another corruption case against him.
Islamists blamed for killed policemen
The killing of 25 Egyptian policemen in the Sinai near the desert border with Israel on Monday was blamed by the new, military-installed government on Islamist militants. State television carried emotional demands for retribution against the Muslim Brotherhood.
The policemen were on their way to their barracks in Rafah when militants attacked them with machine-guns and rocket-propelled grenades, according to security sources. Egyptian state television reported that the presidency announced three days of mourning for the "martyrs of Rafah".
Mounting insecurity in the Sinai worries Egypt and the United States because the desert peninsula lies next to Israel and the Palestinians' Hamas-ruled Gaza Strip, as well as the Suez Canal, one of the world's most important shipping arteries.
US ‘deeply troubled’
The United States voiced concern about the deaths on Sunday of 37 men who authorities said were suffocated by tear gas during a bid to flee custody.
"We are [...] deeply troubled by the suspicious deaths of Muslim Brotherhood prisoners in a purported prison escape attempt near Cairo," State Department spokeswoman Jen Psaki told reporters in Washington.
Having initially defended police action, Egypt later said that two officers had been arrested over the incident.
Egypt's second largest Islamic party, Nour, called in a statement for a presidential decree to create an independent fact-finding committee into the deaths of the 37 men and blamed the interior ministry for the incident.
The United States also urged Egypt not to ban the 85-year-old Muslim Brotherhood, a movement that has long renounced violence and distanced itself from militant groups.
UN Secretary-General Ban Ki-moon called on Egypt to free Morsi, who faced mass street protests as he marked a first year in office on June 30 - or at least ensure a transparent process.
Ban also said "the political space for the Muslim Brotherhood should be expanded, because their political space has been very limited."