The PM told journalists after talks with Egyptian President Husni Mubarak on Sunday that he was certain "there will be a meeting … before the end of February."
Quraya named head of office Hasan Abu Libda and top negotiator Saib Uraiqat as likely candidates to meet Israeli PM Ariel Sharon aide Dov Weisglass on 15 February to complete an agenda.
During a first round of preparatory talks in Jerusalem last week, "all the questions on the [meeting's] agenda were examined, but we did not reach agreement on all the questions."
The Palestinian PM has yet to meet Sharon since his appointment late last year in one of the starkest indications of the deadlock in the Middle East peace process.
But a possible meeting will not please the majority of Palestinians, according to Hamas' spokesman in Lebanon.
Speaking to Aljazeera.net on behalf of the resistance movement, Usama Hamdan said he could see no possible value in a February meeting between the two PMs.
"There is nothing that can possibly be achieved. I do not understand why anyone would want to speak to Sharon in the face of daily Israeli aggression in the occupied territories."
Hamdan said it was more important for Quraya to be involved in rooting out rampant political and financial corruption in the Palestinian Authority and forming a defence force capable of protecting Palestinians.
But talks were encouraged by Mubarak in Cairo, who focused on how to stop Israeli-Palestinian violence and revive peace negotiations.
The possible Sharon meeting comes amid mounting controversy over Israel's West Bank separation barrier which Palestinians believe is a deliberate ploy to pre-empt the boundaries of any future state.
In places, the barrier juts deep into Palestinian territory, but Israel insists it forms a vital part of their defences against resistance attacks.
"I believe that there will be a meeting with Sharon before the end of February"
Palestinian prime minister
The Hague-based International Court of Justice is due to begin hearings into the legality of the Israeli barrier on 23 February.
To the consternation of the Palestinian leadership, several European states have said the court should not pass judgment on such a political issue.
The Cairo visit comes amid a debate over Sharon's plans to evacuate Jewish settlements in the Gaza Strip.
Egypt has welcomed the proposal, but warns that it will not be enough to end more than 40 months of fighting between Israel and the Palestinians.
Quraya is to launch a six-nation European tour with talks with senior Italian officials on Monday before heading to Ireland, current holder of the European Union's rotating presidency.
He will then return briefly to the West Bank before heading back to the continent for trips to London, Berlin, Paris and Brussels.
Also on Sunday, Israeli media sources said Sharon's office manager had initiated contacts with the opposing Labor party concerning the formation of a united national government.
The move is seen as an attempt to forge a national consensus for the PM's controversial disengagement plan which envisages a halt to the road map peace process.