The invitations to all six member Gulf states were sent out, the source said on Wednesday, with the summit due to be held on December 5-6.
The quartet has accused Qatar of funding "terrorism", a charge that Doha has vehemently denied. Kuwait has taken up the role of mediator in the hopes of resolving the crisis.
"As long as Qatar continues this approach, the Kingdom of Bahrain cannot participate in any GCC summit or meeting attended by Qatar unless it corrects its approach, comes to its senses, and responds to the demands of the countries that suffered so much from its policies," King Hamad bin Isa Al Khalifa said on October 31.
Also in October, Sheikh Sabah Al Ahmad Al Sabah, the emir of Kuwait, warned of the collapse of the GCC should the crisis with Qatar continue.
"Any escalation will bring with it an outright call for regional and international intervention, which will destroy the security of the Gulf and its people," he said.
"History and the future generations of Arabs will not forget those who contributed to the escalation of the conflict and caused the destruction of the Gulf."
Established in 1981, the GCC promotes economic, security, cultural and social cooperation between the six states and holds a summit every year to discuss regional affairs.