Abbas's Fatah party and the ruling Hamas party have tried for months to agree on a national unity government, in hope of ending a boycott by the United States and the European Union and in order to present a united front toward Israel.
Washington and Brussels consider Hamas to be a terrorist group and suspended direct financial aid to the Palestinians because the movement refuses to renounce violence or recognise Israel.
Izzat al-Rashq, a Hamas representative, said in an interview with Al Jazeera that the two parties are ready to reach an agreement on the disputed issues.
"The meeting is an attempt to reach final solutions and agreements over a group of proposed cases, between the two sides, which are related to the formation of a national unity government, the ministries and the political programme," al-Rashq said.
"We can send an important and assuring message to the sons of our people that this meeting will help in reinforcing the national unity and avoiding any conflict between the two sides."
Tensions between the two factions, which had already claimed a number of lives, boiled over in the Gaza Strip in December, killing more than 30 people in that month alone.
However, violence has tapered off in the past couple of weeks.
Clashes last month came after Abbas called for early elections as a way of resolving the standoff with Hamas, which rejected the move.
Speculation over meeting
There has been some speculation on whether Abbas would meet Meshaal and the Palestinian president has been non-committal on the talks.
Speaking at a press conference with visiting EU foreign policy chief Javier Solana on Friday, he would say only that he would meet with "numerous Palestinian figures" in the Syrian capital.
In Gaza City, however, Ismail Haniya, the Hamas-aligned Palestinian prime minister, said such a meeting was "expected".
The Palestinian president stopped in Amman on Friday for talks with Peter MacKay, Canada's foreign minister.
MacKay said: "I think we have talked in very constructive and positive ways about what Canada might offer in discussions around the peace, in discussions around negotiations."
The minister, who is also to visit Israel and the West Bank during a regional tour, said he wanted to "meet with other important players here ... and to listen carefully to find a way in which Canada can make a positive contribution".
Following his trip to Syria, Abbas is expected to head on to Beirut.