It will be only the second time the two men have met since Mr Abbas won power.
The Palestinians are expected to make fresh demands for an easing of the pressure the Israeli army exerts on daily life in the occupied territories.
It has occupied the territory for nearly 40 years.
Inevitably, this plan is beginning to loom large over the whole political scene here.
But the Palestinians say that they do not intend to focus on the
Sour atmosphere
Instead they say that the pull-out is already being discussed at lower levels.
The Palestinians see this meeting between the two leaders as a chance to focus on other issues.
Mr Abbas is likely to press for Israeli concessions that would make life easier for Palestinians in the occupied territories.
They include more freedom of movement, more chances for Palestinians to work in
These are familiar Palestinian demands and they are likely to get a familiar Israeli response.
Mr Sharon can be expected to insist very forcefully again that Israeli concessions will only be possible if the Palestinian authorities act to counter militant groups like Islamic Jihad.
Two Israelis have died in the past two days in Islamic Jihad attacks.
The militants say they were responding to what they regard as Israeli violations of a ceasefire.
The violence has further soured the atmosphere here, and nobody is expecting a great deal to emerge from these talks.
PHOTO CAPTION
Mahmoud Abbas and Ariel Sharon