The report said Murei Al Ramthan, accused of operating a cross-border illicit drugs business in southern Syria, was killed in an air raid on a village in Suweida governorate, near the border with Jordan.
Mr Al Ramthan was indicted on drug charges by a Jordanian security court in July last year and given 10 days to turn himself in, according to state television.
His killing was first reported by news sites linked to the opposition to Syrian President Bashar Al Assad.
No government has claimed responsibility for the reported attack and there was no official comment from Damascus.
The incident came a day after Arab League members agreed to reinstate Syria to the body, with one of the conditions being that Damascus act to halt the flow of narcotics to neighbouring countries.
A Syrian opposition figure in Amman, who did not want to be named, told The National that Mr Al Ramthan — a Syrian citizen — was “the most important local border drug player, by far”.
Asked about the raid, Jordan's Foreign Minister Ayman Al Safadi did not explicitly rule out Jordanian involvement.
“When we take any step to protect our national security, we will declare it. We will declare it at the right time,” he said told reporters after a meeting with Dutch Foreign Minister Stef Blok in Amman.
Mr Al Safadi said Jordan was seeking co-operation from the Syrian government to curb drug flows.
On Friday, Mr Al Safadi told CNN that if Jordan did not see Damascus taking “effective measures”, the kingdom “will do what it takes to counter that threat, including taking military action inside Syria”.
Syrian opposition media said Mr Al Ramthan was killed along with seven family members in a strike on his house in the village of Shaab, east of the city of Suweida.
The village is situated in a rugged basalt plain known as the black desert, which constitutes the main part of the drugs corridor between Syria and Jordan.
A second air strike on Monday hit an abandoned drug facility in Syria's southern Deraa province, linked to the Iran-backed Lebanese group Hezbollah, according to Syrian opposition figures.
“Both Al Ramthan's home and the facility were left in ruins,” Ryan Marouf, a Syrian researcher tracking the drug trade, told Reuters.
Jordan has accused the Syrian military and allied pro-Iranian militias of involvement in the smuggling of drugs into the kingdom, mainly the amphetamine known as Captagon.
With western support, Jordan has been beefing up its border with Syria, building fences and trenches and increasing military patrols to stop the flow of Captagon.
The drugs factory in the Deraa town of Kharab Al Shahem was believed to have been a meeting point for Hezbollah-paid smugglers, Mr Marouf said, corroborating accounts by local sources familiar with the matter.
In March, Britain and the US imposed sanctions on the Syrian President's cousins for their alleged role in the manufacture and export of Captagon.
London sanctioned five additional people including businessmen and militia leaders over their ties to the trade.
Drug flows from Syria to Jordan surged after Damascus regained control over most of the border area with Jordan in 2018.
The Syrian military entered the area under a deal between Russia, Israel and the US as Washington and others abandoned or rolled back support for rebels fighting Mr Al Assad.
Southern Syria was the birthplace of the March 2011 revolt against Syrian President Bashar Al Assad, which developed into a civil war by the end of the year, after security forces suppressed the pro-democracy protest movement.
With Russian encouragement, Jordan began an accommodation with Mr Al Assad two years ago, lifting some restrictions on trade with Syria.
Jordan also supported the return of Damascus to the Arab League on Sunday, partly in the hope of action by the regime to curb the cross-border drug flows, Jordanian officials said.