Free Syrian Army commander Ahmad Hijazi said the reward would be paid by Syrian businessmen who support the army, Turkey's state-run Anadolu Agency reported Tuesday.
The reward is for Bashar "dead or alive," the army official said.
Hijazi declined to name the businessmen for their protection.
Meanwhile, Syrian government forces pounded villages, including those along the country's border with Turkey.
Anadolu reported Tuesday three people were killed in aerial bombings in Iral and Siverin, where a mosque, several houses, a cemetery and a school were damaged as well.
In Syria's capital of Damascus, residents who don't support either side claim they're caught in the middle of the civil war that began in March 2011, CNN reported.
"Every day, we are hearing this boom, boom and everything else, but there is life that is going on," Rama Hamdi told the broadcaster in an interview at a salon. "I am worried sick about it, but there is nothing we can do."
Several shopkeepers said business is down, despite a bustling marketplace. They told CNN they were concerned about talking on camera about their situations because they didn't know how the government or rebels would react.
"Nowadays, I cannot go to the countryside without being worried someone will stop me," said Rauda Alaita, the salon's owner. "Is it the real army or the other army stopping me? What answer should I answer them with [about] who I am? Now it's really difficult because you are stuck in the middle."
During a recent news conference, opposition figures called for talks with the government, but one key opposition player, the Free Syrian Army, was absent because members knew they'd be arrested, CNN said. Participants at the news conference were from opposition groups the government tolerates.
At least one said the tolerated opposition groups know they're powerless.
"We are demanding from the regime ... guarantees for the safety of this opposition to come in," Mazen Bilal told CNN, "but we can't impose this on the regime."
The Syrian Network for Human Rights said Tuesday it documented the death of 132 people in several Syrian provinces, including 14 children, seven women, and four who exhibited evidence of being tortured.
Forty-five deaths were reported in Damascus and surrounding areas, the organization said in a release. The organization said 28 people died in Aleppo, 27 in Daraa and 12 in Idlib.
Most of the victims were "killed by armed forces" or by "random shelling," said the organization, which also posted links to several YouTube videos as further documentation.