One of the scholars said they would offer their services to the government in their forthcoming meeting with the Crown Prince, the kingdom's de-facto ruler.
"A meeting with crown prince and a group of more than 40 Saudi scholars is scheduled over the next three days in Makka to consider mediation," the scholar Safar-al-Hawali told Asharq al-Awsat newspaper.
"This initiative aims to stop any new terrorist attack, to stop the bloodshed and to open a dialogue between the government and the extremists as well as the wanted armed men," he said.
"A meeting with crown prince and a group of more than 40 Saudi scholars is scheduled over the next three days in Makka to consider mediation"
Interior Minister Nayif bin Abd al-Aziz Al Saud has however scoffed at the mediation initiative.
"We can talk to them only with the gun and the sword," he said of those behind the attacks.
Saudi monarch King Fahd bin Abd al-Aziz Al Saud had also delivered a tough message, threatening to deal with an "iron fist" those responsible for the attacks.
Authorities in Saudi Arabia have launched a major crackdown on suspected al-Qaida elements in recent months.
The crackdown is expected to intensify after Sunday's bombing of a residential compound in Riyadh's outskirts, that killed 17 people and wounded 122 more.