Citing Israeli political sources, Haaretz newspaper said in its online edition on Saturday that the leaders would hold talks at the end of the month, after they returned from a 14-16 September summit at the United Nations.
The Haaretz report referred to the meeting in the context of Israel's withdrawal from Gaza Strip.
The pullout stirred hopes of new progress on a road map to peaceful Palestinian statehood.
Abbas had called the move a "brave and historic decision" and voiced hope that it would "open a new page ... for the sake of peace and the future of both peoples and the region".
Sharon and Abbas held their first summit in February, soon after Abbas won elections to succeed the late Palestinian leader Yasser Arafat.
They declared at that summit a ceasefire seen as key to Israel's plan to remove settlers from occupied land.
At a second meeting, in Jerusalem on 21 June, the two cemented an agreement to coordinate the Gaza pullout, but failed to bridge differences on other issues such as the Palestinian leader's request for other confidence-building measures.
Jewish settlements have been
destroyed in Gaza
Meanwhile, in remarks published on Saturday, Abbas said even after its Gaza military pullout, Israel will be occupying some Palestinian land in the coastal strip.
Abbas spoke just two weeks before Israel was to withdraw its last soldiers from Gaza, after the demolition of 21 Jewish settlements there.
The Palestinians contend that several border crossings were built by Israel on Gaza land and should be moved as part of the pullout.
"There are lands in eastern and northern Gaza still under occupation," Abbas said in an interview published on Saturday in the Palestinian daily Al Quds. "There are differences and agreements over borders.
"We need to renegotiate the details and get back to the real border," Abbas said, referring to the frontier between Israel and Gaza that existed before the 1967 Middle East war.