The report published Monday by the French daily Le Figaro said two air corridors -- one in the south of Jordan from the Negev region in southern Israel and another north of Amman -- have been made available to the Israeli air force.
Israel has stated concerns over the situation in Syria, including jihadist elements operating near its border and chemical weapons stockpiles in the country, the newspaper said.
Abdullah's decision threatens the fragile situation Jordan is facing due to thousands of Syrian refugees in Jordan, Le Figaro said. Their presence in Jordan has affected the country's economy.
The newspaper said Syrian President Bashar Assad has rejected all proposals for a cease-fire and in a recent television interview issued a veiled warning to Jordan.
"The fire will not stop at our borders. Everyone knows that Jordan is also exposed [to the crisis] that Syria knows," Assad was quoted as saying.
Neither Israel nor Jordan officially commented on the Le Figaro report.