As a result of the anti-government uprising there, Hamas was said to be looking for another home, The New York Times reported Monday.
Hamas officials denied a report appearing in a London-based Arab newspaper Saturday that Hamas' political wing was leaving for Doha, the capital of Qatar.
Similar reports circulating Monday were also denied by Hamas.
However, Hamas officials have acknowledged difficulties in relations with Syrian authorities.
"The Syrian government said to us, 'Whoever is not with us is against us,'" a senior Hamas official at a Palestinian camp near Damascus said. "It wants us to express clearly our position over what is going on in Syria. It wants us to be against the Syrian demonstrations.
"We told them we are neutral. We said to them we are living in the country as visitors and we have no right to comment or interfere in the country's problems," the official said.
Syrian security forces have killed about 500 demonstrators in anti-government protests inspired by similar actions across the Arab world.