Justice Minister Ahmed Mekky was mediating negotiations between Morsi and members of the Supreme Judicial Council, BBC News reported.
One possible way out of the crisis would be for a memorandum or amendment defining the decree's limits, although several prominent opposition leaders have said they will not engage with Morsi until the decree is rescinded.
Meanwhile, stocks in Egypt continued to tumble Monday.
According to Reuters, the stock market is down 7 percent, with the country's main index down 3.9 percent right after it opened.
More than 500 people have been injured in protests since Morsi issued the decree on Thursday, which shields his decisions from becoming subject to judicial review.
From Cairo, GlobalPost's Erin Cunningham reported that Egyptians are concerned about the direction protests may take.
"There is some talk about businesses closing early tomorrow because of mass anti and pro-Morsi protests planned for Tuesday, and that could lead to violence. People have warned of a "second revolution" plenty of times before and everything passed more or less uneventfully. But people are worried," she wrote from the city's Zamalek neighborhood.
She added that the unrest has appeared to stay confined to Tahrir Square.
"Today, I was not in the area where protests were taking place. Though it's also important to note that because Cairo is such a vast city, that even if clashes are occurring in Tahrir Square or its environs, life outside the square goes on as normal. From where I am today, I haven't seen any indication of the unrest or instability," she wrote. "Tahrir Square is a bubble in that sense."
Morsi's administration has defended his decree as an effort to speed up reforms and complete a democratic transformation. However, leftists, liberals, socialists and others say it has exposed the autocratic impulses of a man once jailed by Mubarak.
Erin Cunningham contributed reporting from Cairo.