Opposition media reported the jet crashed near Khan Sheikhoun, close to the frontlines of the regime offensive.
Hardline rebels in Idlib claim they shot down a Syrian regime Sukhoi 22 warplane on Wednesday.
The statement from Hayat Tahrir Al Sham, a former Al Qaeda affiliate, said the jet was hit over the town of Al Tamanah in southern Idlib, where a grinding offensive by the Syrian military has displaced thousands.
Orient, a pro-Syrian opposition TV station, also reported that a jet had been downed and said that the incident took place near Khan Sheikhoun, close to the frontlines of the regime offensive. Khan Sheikhoun is nine kilometres from Al Tamanah.
Regime fighters pushed further into the extremist-run bastion in northwest Syria on Wednesday, inching towards a key town after months of deadly bombardment, a monitor said.
Eight years into Syria’s civil war, the militant-run region of Idlib is the last major stronghold of opposition to President Bashar Al Assad’s regime.
Air strikes and rocket fire by the regime and its ally Russia have pounded Idlib for more than three months, killing hundreds and displacing tens of thousands.
In the south of the stronghold, fighting has neared Khan Sheikhoun, which lies on a highway coveted by the regime.
A sarin gas attack on the town in 2017 killed dozens of people and prompted President Donald Trump to order a missile strike against the Syrian airbase from where the United States said the attack had been launched.
An investigation by the United Nations and the Organisation for the Prohibition of Chemical Weapons said the Syrian government was responsible for releasing sarin on the town on April 4, 2017. Damascus denies using such weapons.
Almost all residents of Khan Sheikhun have since left the town.
After a week of ground advances, Mr Al Assad’s fighters were a few kilometres away from the town on Wednesday, the Syrian Observatory for Human Rights said.
“Regime forces are now four kilometres from Khan Sheikhun to the west, with nothing between them and it but fields,” Observatory chief Rami Abdel Rahman said.
To the east, pro-Assad fighters are battling to control a hill six kilometres from the town, the head of the Britain-based Observatory said.
Clashes on Wednesday have killed 14 regime forces, 20 extremists and seven allied rebels, he said.
State news agency Sana on Wednesday said troops had taken several villages from the militants in the area west of Khan Sheikhun.
AFP correspondents have reported seeing dozens of families flee fighting over the past few days, heading north in trucks piled high with belongings.
A buffer zone deal brokered by Russia and Turkey last year was supposed to protect the Idlib region’s three million inhabitants from an all-out regime offensive, but it was never fully implemented.
An alliance led by fighters from Syria’s former Al Qaeda affiliate — Hayat Tahrir Al Sham — took over full control of the anti- Assad stronghold in May.
Regime and Russian air strikes and shelling since late April have killed almost 820 civilians, the Observatory says.
The UN says dozens of health centres and schools have been targeted.
Humanitarian workers have said that any full-blown ground attack on Idlib would cause one of the worst humanitarian disasters of Syria’s war.
The conflict has killed more than 370,000 people and displaced millions at home and abroad starting with the brutal repression of anti-regime protests in 2011.