The al-Sharq al-Awsat newspaper on Wednesday quoted unnamed officials saying that one of the two Saudis believed to be involved in Monday's attack had a prior security record. The officials say DNA tests are being performed to confirm the attackers' identities.
The pan-Arab daily has close ties to the royal family. It is published by a firm whose chairman is the son of Saudi Arabia's crown prince.
The attack on the Saudi security patrol near the country's border with Iraq killed three soldiers and wounded at least three more. All four militants died. No group has claimed responsibility.
In a separate incident, On Sunday Iraq border guards managed to repel an ISIS attack on a border station between Iraq and Saudi Arabia. Clashes leaves 2 killed in terrorist group and wounding four others.
Brigadier Al Balawi was one of three border guards, including the commander in chief, killed in the attack. Four attackers also died.
The incident occurred when the guards captured one of the men as he approached the border about 4.30am. He detonated an explosives belt, killing himself and two of the guards, the Saudi Interior Ministry said.
The others were killed during an exchange of fire, Saudi officials said.