The meeting will kick-start the renewal of peace talks between the two sides amid increased hopes for a breakthrough in the Middle East.
"The meeting will apparently be during the week of February 8, with the objective being to make progress between both sides, contingent on continued efforts by the Palestinians to prevent terrorism to Israel," Israeli spokesman David Baker said.
The meeting is expected to coincide with new US Secretary of State Condoleezza Rice's visit to the region.
Abbas' plans to ask Sharon for further steps, such as halting Israel's construction of Jewish settlements and its West Bank barrier, Palestinian cabinet minister Ghassan Khatib said.
It would be the first meeting between the two since Abbas was elected to succeed Yasir Arafat as Palestinian president on 9 January.
Abbas wants Israel to stop
building the separation barrier
Hopes for Middle East peace have increased in recent days after a sharp reduction in violence.
Israel has announced it would reduce military raids and assassinations in response to Abbas' efforts to rein in Palestinian resistance groups.
Abbas has ordered the deployment of Palestinian security forces in Gaza to stop resistance fighters from launching rockets and mortar attacks against Israelis.
Israeli Defence Minister Shaul Mofaz and former Palestinian security chief Muhammad Dahlan met in Tel Aviv on Saturday to discuss the ceasefire, as well as further security coordination, such as Israeli pullbacks from Palestinian towns.
After the meeting, a Palestinian political analyst held out hope for the ceasefire. Hani al-Misri told Aljazeera on Saturday: "The opportunity of the truce would be successful as there have been consecutive Palestinian steps confirming the readiness of the Palestinian side."
Twenty-two Palestinians were injured on Saturday in a refugee camp just south of Gaza City during clashes between supporters of the resistance group Hamas and backers of the dominant Fatah party.
Witnesses and medics said the disturbance broke out in the al-Mughazi refugee camp when Fatah supporters holding a rally to celebrate the party's win in the local elections in the camp ran into a group of Hamas supporters who were celebrating the group's overall victory in the Gaza Strip.
Medics said 22 people were injured, five of them by gunfire.
Hamas won 77 of the 118 seats in Thursday's municipal elections in Gaza. Fatah managed to win only 26 seats.