The publication refers that it received optimistic signals in contacts outside the media between Lebanon and Israel.
If there is a restart, the source says, it will be a sign that the US mediation for the negotiations has borne fruit and growing tensions on both sides have eased.
Lebanon and Israel began a round of talks in October to seek consensus about a disputed maritime area with the potential to be rich in oil and natural gas.
However, they were put on hold after Beirut requested to extend claims by 1,430 square kilometers, which began over 860 square kilometers offshore in the Mediterranean Sea.
For that reason, the meetings stopped between the two countries that lack diplomatic relations and are technically still at war.