Parliament was due to meet on Friday (local time) in another attempt at electing a successor to former president Emile Lahoud, whose term ended last week.
The vote has already been postponed five times because leaders of the Western-backed ruling coalition and the opposition, led by Syrian-backed Hezbollah, have been unable to agree on a compromise candidate.
The sources said the lack of agreement meant that opposition MPs would stay away from Friday's session and force another delay. Opposition MPs need to attend the assembly to secure the two-thirds quorum needed for a vote.
"There has been no meaningful talks between the two camps in recent days," a senior political source said.
"There will be no session on Friday to allow for the resumption of contacts."
Asked whether there could be an election this week, another source said: "No way."
Prime Minister Fouad Siniora's Cabinet assumed the powers of head of state on Saturday after Mr Lahoud's term ended with no deal, despite French-led mediation efforts.
Opposition disputes the legitimacy of the anti-Syrian Government and says it has no right to assume the powers of president.
Mr Siniora urged calm this week and said he would not make any "provocative" moves.
Although there has been no deal on Mr Lahoud's successor, the rivals have not carried out threats of unilateral action, and instead have contained the worst crisis since the 1975-1990 civil war.
The presidency was last left vacant in 1988-1989. The crisis triggered one of the bloodiest phases in the civil war. © 2007 Australian Broadcasting Corporation