Independent confirmation of any relaxing of the blockade imposed last week has not yet been available.
The flight ban came as part of a diplomatic boycott of Qatar by Gulf states which has blockaded the peninsular state.
Egypt - along with Saudi Arabia, Bahrain and the UAE - accuse Qatar of funding terrorism and having close relations with regional rival Iran.
Doha has vehemently denied the claims, saying the allegations put forth by its fellow GCC members are baseless.
Egypt has had close relations with the UAE and Saudi Arabia following the 2013 overthrow of President Mohamad Morsi in a military coup.
On Monday, Doha sought the help of the UN's aviation agency after three Gulf states closed their airspace to Qatari planes.
Qatar is home to around 350,000 Egyptians, many of whom travelled to the Gulf state in search of work.
Despite the blockade enforced on Qatar by several key regional players, Doha remains confident of its economy's ability to weather the crisis.
"Our reserves and investment funds are more than 250 percent of gross domestic product," Qatari Finance Minister Ali Sherif al-Emadi told CNBC television in an interview broadcast on Monday.
"I don't think there is any reason that people need to be concerned about what's happening, or any speculation on the Qatari riyal."
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