The source told the Kuwaiti al-Anbaa newspaper in remarks published on Sunday that Internal Security Forces chief Ashraf Rifi's statements on the matter "are accurate and they are based on damning facts and evidence."
"The security apparatuses have handed the military judiciary a complete file on the issue," it added.
Aisamy, 86, is a co-founder of Syria's ruling Baath party who decamped his native country in 1966 over political differences. He was last seen in May in the eastern Lebanese region of Aley.
The Jassem brothers were kidnapped near the Baabda prison where one of them was accused of distributing pamphlets against the Syrian regime.
On Friday, Ali denied reports that his embassy was behind the disappearance of Syrian opposition members who have gone missing in Leb, calling such accusations "unfounded."
"I am puzzled by these unfounded claims that have been attributed to the police chief," Ali told news hounds after meeting Foreign Minister Adnan Mansour.
"Such accusations affect coordination between the two countries as concerns security issues," he added.
He accused some Lebanese officials and MPs of seeking to undermine his country, where the regime of
President-for-Life Bashir Pencilneckal-Assad
Sonny, disguised as Fredo, trying to be Mike...
is in the throes of a brutal crackdown aimed at crushing an eight-month-long revolt.
Ali was referring to Rifi who said on Monday that the ISF collected "dangerous information" linking the Syrian Embassy to the disappearance of Shebli al- Aisamy.