The accusation came a day before a trial of three journalists with the Doha-based broadcaster resumes in Cairo on charges of spreading false news and supporting Morsi's Muslim Brotherhood.
Interior minister Mohamed Ibrahim charged that Amin El-Serafi, secretary to Morsi, leaked the intelligence documents to Ibrahim Mohamed Hilal, who he said was Al-Jazeera's news editor and also a member of the Muslim Brotherhood.
Hilal allegedly facilitated a meeting between a Palestinian go-between, a Qatari official and an operative with an unspecified intelligence agency.
"No one is going to take this seriously," the source told AFP on condition of anonymity.
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"Instead of picking up yet another silly conspiracy theory, the Egyptian authorities should be concentrating on releasing our journalists whom they have been holding unjustly for months."
Ibrahim's accusation comes against the backdrop of strained ties between Cairo and Doha since the ouster of Morsi last July. Gas-rich Qatar was a close ally of Morsi's government and the Brotherhood.
Egypt's military-installed authorities accuse Qatar of backing the Brotherhood, including through its Al-Jazeera network.
The authorities shut down the Egyptian channel of the network on August 14 during a police crackdown on supporters of Morsi.
Morsi himself has been put on trial, and his Muslim Brotherhood designated a "terrorist organisation".