The majority March 14 bloc and the Hezbollah-led opposition have been locked in a bitter power struggle since November 2006, when Hezbollah and its allies pulled its members out of the March 14-led cabinet.
Relations between the two sides have further deteriorated since the presidential term of Emile Lahoud, who is widely perceived to be a pro-Syrian figure, ended in November 2007.
The March 14 bloc, which is widely considered to be pro-Western in its outlook, and Hezbollah, which has close links to Syria and Iran, have been unable to agree on a new president.
Lebanese deputies are due to hold a parliamentary session on Tuesday to elect a successor to Lahoud.
The vote has been postponed on 14 occasions, highlighting the continued deadlock between March 14 and the opposition.
The pan-Arab Al Hayat newspaper reported on Monday that Hosni Mubarak, Egypt’s president, and King Abdullah of Saudi Arabia said a new Lebanese president should be chosen before an Arab League summit in Syria in late March.
Ahmed Aboul Gheit, Egypt's foreign minister, said last month that the success of the upcoming summit in Damascus was largely dependent largely on Lebanese leaders agreeing on a new president.
Moussa has already visited on several occasions to try to get Lebanese leaders to agree on electing General Michel Suleiman, commander of the Lebanese army, as a compromise candidate for president.
The Arab League plan, which was adopted unanimously by Arab foreign ministers in Cairo last month, also calls for a national unity government and the adoption of a new electoral law.
The United States and the March 14 bloc say that Syria has sought to block the presidential election, a charge denied by Damascus.