Sheik Hamad bin Khalifa Al Thani's comments to CBS "60 Minutes," which will be aired Sunday, are the first statements by an Arab leader calling for the deployment of troops inside Syria.
They come amid growing claims that a team of Arab observers dispatched to the country to curb the bloodshed has failed in its mission.
Asked whether he is in favor of Arab nations intervening in Syria, Sheik Hamad said, "For such a situation to stop the killing some troops should go to stop the killing."
Excerpts of the interview were sent to The Associated Press by CBS a day before it was to be aired.
Qatar, which once had close relations with Damascus, has been a harsh critic of the 10-month crackdown by President Bashar Assad's regime. The wealthy and influential Gulf state withdrew its ambassador to Syria in the summer to protest the killings.
Arab League observers began work in Syria on Dec. 27, to verify whether the government is abiding by its agreement to end the military crackdown on dissent.
But far from bringing a halt to the violence, the mission has coincided with an apparent increase in killings. A UN official said Tuesday that about 400 people have been killed in the last three weeks alone, on top of an earlier estimate of more than 5,000 dead since March.
Opposition and army defectors meanwhile have increasingly been taking up arms to fight back.
On Friday, Arab League chief Nabil Elaraby warned that Syria may be sliding toward civil war. Elaraby said Assad's regime was either not complying or only partially complying with an Arab League peace plan.
The plan calls for removing Syrian heavy weapons from city streets, starting talks with opposition leaders and allowing human rights workers and journalists into the country.
The mission has been plagued by problems, including accusations that the Syrian government is interfering with the team's work. This week, one of the observers resigned and told the pan-Arab TV channel Al-Jazeera that the monitor mission was a "farce" because of Syrian government control.
On Saturday, Lebanese officials said a man was killed by a bullet coming from the Syrian side of the border. The officials said Lebanese citizen Hassan Obeid, 17, died in a clinic where he was rushed after being hit in the stomach in his northern hometown of Bkarha near the border with Syria.
The officials spoke on condition of anonymity as they were not authorized to talk to the press.
Several Lebanese and Syrian citizens have been killed in border areas in Lebanon since the uprising against Assad began.
More than 5,000 Syrians have fled to Lebanon during the uprising.
In the restive central city of Homs, the British-based Syrian Observatory for Human Rights said, troops at a checkpoint opened fire randomly on Saturday, killing two people.