The Grand Imam of al-Azhar, Sheikh Ahmed al-Tayyib, had invited different political forces to talks.
However, a spokesman for the Muslim Brotherhood's Freedom and Justice Party questioned the imam's impartiality.
Egypt has been polarised since the army deposed Mr Morsi after mass protests.
"We are ready to do any kind of dialogue with any intermediary," Mohammed Soudan, foreign affairs spokesman of the Freedom and Justice Party, told the BBC's Newshour programme.
However, he pointed out that the grand imam had openly supported the military intervention to remove Mr Morsi on 3 July.
Mr Soudan also said that before talks, the party wanted the release of high-ranking Brotherhood officials arrested in a crackdown on the movement which took place after Mr Morsi was ousted.
'Ready to be killed'
Political tensions have been growing in recent days with the interim government saying that international mediation efforts had failed and numbers swelling at two pro-Morsi protest camps in Cairo.
The military-backed interim government has said police will clear the sites in the coming days, raising fears of bloodshed. Unnamed security sources have said that the move against the camps might begin on Monday.
More than 250 people, most of them Morsi supporters, have been killed in clashes since the military deposed Egypt's first democratically elected leader following mass protests demanding his resignation.
Mr Soudan said that the protesters demanding Mr Morsi's reinstatement would not leave the camps "unless we get our dignity back".
"Those people really are ready to be killed at any second. This is the mentality now of the people who are sitting in both Rabaa al-Adawiya and al-Nahda square," Mr Soudan said.
Al-Azhar, a highly respected institution, has had some success at unifying different political forces since the 2011 uprising that toppled President Hosni Mubarak, reports the BBC's Yolande Knell in Cairo.
However on this occasion its task is exceptionally difficult, our correspondent says, given then grand imam's open support for Mr Morsi's removal and the current depth of division between the two sides.
Last week, Egypt's interim President, Adly Mansour, blamed the Muslim Brotherhood for the failure of mediation efforts by international diplomats, as well as "consequent events and developments relating to violations of the law and endangering public safety".
Before the four-day holiday of Eid al-Fitr, which marks the end of the Islamic holy month of Ramadan, interim Prime Minister Hazem Beblawi announced that the decision to disperse the pro-Morsi sit-ins outside the Rabaa al-Adawiya mosque and the al-Nahda square near Cairo University was final.
On Friday, Brotherhood leader Mohammed al-Beltagi warned the government: "Kill as much as you like. I won't move an inch… We will offer a million martyrs."
The statements prompted new calls for restraint from the international community.
Also on Sunday, the army said it had killed at least eight suspected militants in a strike in the Sinai peninsula.
According to a statement from an army spokesman, those targeted were involved in the killing of 16 Egyptian border guards in August last year.
The Sinai region has become increasingly lawless since President Mubarak was ousted in 2011.
Islamist militants in northern Sinai have used the lack of central authority to base themselves there and carry out attacks across the border into Israel.