According to the source, Syrian President Bashar Assad has refused to meet with Hamas politburo chief Khaled Mashaal after the latter called for reforms in Syria following the oppression of opposition protestors.
Hezbollah Secretary-General Hassan Nasrallah's attempts to mediate between the two have been futile.
The source noted that apart from Mashaal, the movement's leaders have left Syria in favor of several countries.
Mashaal's deputy, Moussa Abu Marzouk, reportedly left Damascus for Amman. According to the source, Jordan agreed to take him in under the condition that he avoids engaging in any political activity on its territory.
The Hamas leadership was deported from Jordan about a decade ago before settling in Syria.
Nasrallah meets with Assad, Mashaal left out (Photo: AP)
According to the newspaper, Mashaal has yet to leave Syria officially, but Qatar is holding talks behind the scenes with several countries, led by Jordan, to take him in.
The talks being held with Jordan have been positive, the report said, and Mashaal may be welcomed there as long as he meets conditions regarding his activity.
According to the source, the tensions between Damascus and Hamas began before the start of the Syrian unrest. Upon the start of the Arab Spring, Mashaal suggested that Assad carry out reforms in a bid to prevent the uprising from reaching his country.
After the riots in Daraa began, Mashaal met with senior political and military officials in Syria and stressed the need to solve the issue and punish those responsible for the killing. They suggested that he approach Assad directly.
The Hamas leader tried to set a meeting with the Syrian president, but received no response.
The source noted that following the incident, Mashaal traveled to Lebanon for a secret meeting with Hassan Nasrallah, during which he urged the Hezbollah leader to intervene and advise Assad to respond immediately to the protestors' demands.
Mashaal stressed that Hamas could not stand by the Syrian leadership in light of the bloodbath taking place in the country.
Nasrallah, the source said, told Mashaal that he would ask for a three-way meeting with Assad, but the Syrian president decided to meet with the Hezbollah leader alone.
Nasrallah promised to update Mashaal on his meeting with Assad, but left Damascus without meeting with the Hamas leader. Later on, he sent a delegation to inform Mashaal that his letter had been delivered to Assad.
The source noted that Iran had intervened as well in order to pressure Hamas, and even suspended its monthly financial aid to the movement, leading to an economic crisis in the Gaza Strip.
According to the source, one of the Gulf countries (whose name he did not mention) was now transferring money to Hamas instead of Iran.
He added that Hezbollah had also considered distancing itself from the Syrian regime over the Syrian violence, but decided to declare its support for Assad following heavy Iranian pressure.