The official Syrian news agency said al-Asad had lunch with the amir in Damascus, but gave no more details.
A diplomat, speaking before the meeting on Wednesday, said the talks would focus on Lebanon and Syrian-US relations.
Al-Asad is also expected to fly to Saudi Arabia within 48 hours for emergency talks on Lebanon, a leading Saudi newspaper reported.
Saudi Arabia and Qatar are key US allies in the region.
The Al-Riyadh daily on Wednesday quoted an Arab diplomatic source in Riyadh as saying al-Asad would arrive either on Wednesday or Thursday for a meeting with the Saudi government, whose agenda would also include other issues in the Arab region.
Qatar's Amir had lunch with
al-Asad on Wednesday
A Saudi Foreign Ministry spokesman could not confirm if the visit was planned. In Damascus, Syrian officials were not immediately available for comment.
Analysts and diplomats say Syria is seeking the help of friendly Arab countries who are allies of the United States to deflate mounting pressure over its military and intelligence presence in Lebanon.
Syria's ambassador to London, Sami Khiyami, told BBC radio on Tuesday that the withdrawal of Syrian troops from Lebanon was under consideration by Syria, Lebanon and other Arab nations such as Saudi Arabia and Egypt.
For his part, al-Asad said in an interview with Time magazine published on Tuesday that Syria could withdraw its 14,000 troops in a few months.
The Syrian-backed Lebanese government collapsed earlier this week after two weeks of protests triggered by the assassination of former Prime Minister Rafiq al-Hariri.
Damascus denies involvement in his death and a bombing last week in Israel.