The matter will be heard by a bench headed by Chief Justice Ranjan Gogoi along with Justice S.A. Bobde, Justice D.Y. Chandrachud, Justice Ashok Bhushan and Justice S. Abdul Nazeer.
The court was hearing an application filed by Gopal Singh Visharad, one of the parties representing the Hindu community.
He moved the Supreme Court on July 9 to list the Ayodhya dispute for adjudication saying there has been no progress in the mediation process.
His counsel and senior advocate P.S. Narasimha contended that not much progress had been made in the first round of mediation process, which was initiated by the top court.
If mediation fails, then the Supreme Court may begin day-to-day hearing in the dispute, said the apex court on July 11.
On May 10, the Supreme Court extended the term of the mediation committee on the Ayodhya dispute till August 15.
The court said the members of the committee were not experiencing any difficulty in the mediation process.
It observed that the Chairman of the committee, former Supreme Court judge F.M.I. Kalifulla had indicated progress in mediation so far and sought extension of time to complete the task.
The court refused to divulge the details on the mediation efforts.
"We will not tell you the progress made, that is confidential," replied the court to a counsel's query regarding the mediation. The court observed that the mediation process can also be extended, if required.
The court's observation has come after a report was submitted on the mediation efforts.
The top court had on March 8 set up a three-member committee to mediate to find a possible settlement of the Ram Janmabhoomi-Babri Masjid Ayodhya title dispute.
The Kalifulla panel has Art of Living founder Sri Sri Ravi Shankar and senior advocate Shriram Panchu as its other members.
The mediation is taking place at Faizabad, near Ayodhya.
( With inputs from IANS )