The Egyptian Foreign Ministry was quick to dismiss the reports published in Israeli media, saying the initiative was actually made in the past by ousted Islamist President Mohammed Morsi.
Sisi, too, denied such reports and said there is no Egyptian proposal to offer parts of the Sinai to Palestinians to create a new state.
"No one can do this (cede parts of the Sinai Peninsula for a Palestinian state)," he was quoted by Egypt's official MENA news agency as saying.
Under the terms of the purported plans, the Palestinian Authority would be granted full autonomy in Palestinian towns and villages in the West Bank.
More From This Section
In exchange, Abbas was asked to relinquish his demand that Israel retreat back to pre-1967 borders.
The report added that the Egyptian initiative received the US' go-ahead. Israel's Prime Minister Benjamin Netanyahu was also informed.
According to the report, Sisi said to Abbas in the meeting: "You are now 80 years old, if you don't accept this proposal, your successor will."
Gaza is still recovering from a 50-day conflict which saw more than 2,100 Palestinians killed as well as 66 Israeli soldiers and seven civilians.