Sisi told state newspaper editors that he believed Israel was increasingly convinced of the need for a peace deal, saying it was a "positive sign."
But Palestinian infighting between the Islamist Hamas rulers of Gaza and Palestinian president Mahmud Abbas's Fatah in the West Bank remained an obstacle, he said in the interview.
Talks between Israeli Prime Minister Benjamin Netanyahu and Abbas have been suspended since 2014, despite a push by Washington and France to resume the peace process.
Sisi, who is seen as having good ties with both Israel and Abbas's Palestinian Authority, has also been pushing for a resumption of negotiations.
"Putin has told me that he is ready to receive both (Abbas) and Netanyahu in Moscow to carry out direct talks to find a solution and solve the issue," Sisi said.
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"I see that the conviction of the importance of peace is rising among the Israeli side, and the conviction about finding an exit to the issue is a positive sign.
"At the same time, it is important to end the Palestinian-Palestinian rift... and to have national reconciliation between the Palestinian Authority and Hamas so that the climate be ready for real efforts to establish a state," he said.
Sisi said last month that his country was making serious efforts to break the deadlock between Israel and the Palestinians.
His remarks followed a trip by Egypt's Foreign Minister Sameh Shoukry to Israel, the first in nine years.
Egypt became in 1979 the first Arab country to sign a peace treaty with Israel, after four wars.
Netanyahu has called on Palestinians to engage in direct negotiations with Israel, but Palestinian leaders say years of talks have not ended Israel's occupation of the West Bank.
Abbas has instead tried to put pressure on Israel through diplomacy at the UN.