The sources described the situation as a "silent crisis" between the two senior Palestinian officials, the London-based Arabic newspaper said.
Tensions between the men escalated after Fayyad refused to deliver a letter from Abbas to Israeli Prime Minister Binyamin Netanyahu in Jerusalem Tuesday.
In his letter, Abbas detailed his conditions for a renewal in talks. He called on Israel to halt settlement construction, demanded that Israel accept the June 5, 1967, lines (its borders before the Six-Day War that year) as a basis for a future agreement and called for the release of Palestinian prisoners held before the signing of the 1993 Oslo Accords.
Because of Fayyad's refusal to meet Netanyahu, Abbas was forced to send others, including Palestinian negotiator Saeb Erekat, the report said. The incident caused Abbas great embarrassment, the newspaper said.
Since then, Abbas has refused to accept Fayyad's telephone calls or schedule a meeting with him, the report said.