Public radio, as well as several local newspapers, said Israeli and Jordanian officials had confirmed the meeting, which was first reported in the Al-Quds al-Arabi daily on Wednesday.
A spokesman for Netanyahu declined to comment on the reports.
The date of the meeting has not been reported, but Israeli media said the meeting focused on the regional threat posed by Syria’s chemical weapons stocks.
“Both sides arrived at the meeting with maps in hand,” the Yediot Aharonot daily said. “Their maps marked the various sites across Syria where the forbidden weapons are being stored.”
The newspaper cited Jordanian officials as saying the king and Netanyahu “raised situation assessments about the ‘day after Assad,’ and examined the danger posed by the chemical weapons in Syria to the neighbouring countries, first and foremost Jordan and Israel.”
The meeting also touched on Jordan’s attempts to kickstart negotiations between Israel and the Palestinians, with the monarch urging Netanyahu to renew discussions directly after a general election on January 22.
“At this stage it is not clear what this Israeli-Jordanian brainstorming is going to produce,” analyst Smadar Peri wrote.
“The entire world wants (Syrian President Bashar) al-Assad gone, but Israel and Jordan — as well as Turkey and Lebanon — are going to have to deal with what he might do in his final moments in power.”
Assad’s stocks of chemical and biological weapons remain a primary concern for Syria’s neighbours as well as for much of the international community.
Assad’s regime has insisted it would never use the weapons against its own people, but as violence between the regime and rebels seeking its overthrow rages on, there are fears an embattled leadership could unleash the weapons.
The international community also fears the weapons could be transferred to or seized by militant groups.