A bench of justices R V Raveendran and A K Patnaik also proposed the appointment of a curator of a museum to preserve the treasure being unearthed from the centuries-old temple.
The apex court's directions came during the hearing of a petition by the heir of the erstwhile king of Travancore Raja Rama Varma, challenging a Kerala high court ruling of January 31 this year, ordering the takeover of the assets and management of the shrine by the state.
The court also barred the observer, supervising the unearthing of the temple's treasure, from giving any interview about the process, saying the matter is related to the state.
After brief proceedings, the court posted the matter for further hearing on Friday.
Earlier, on May 2, on a petition filed by Rama Varma's elder brother Marthanda Varma, the apex court, by an interim order, had stayed the high court's order for takeover of the management and assets of the temple.
While hearing of the petition, the court had directed that "there shall be a detailed inventory of the articles, valuables and ornaments found from the temple's treasure trove."
The court had also appointed retired judges of Kerala high court, Justices M N Krishnan and C S Rajan, as observers to supervise unearthing of the temple's treasure and had said that the inventory list would be prepared in their presence.
The two petitioners in the matter, including Marthanda Varma, were also authorised by the apex court to be present during the preparation of the inventory list.
The court had also said the inventory shall be made in the presence of the devaswom department's secretary or a representative nominated by it.
The court had also directed the presence of a senior officer of the department of archaeology during the preparation of the inventory list.
The court had also made Justice Krishnan as the in-charge for organising the inventory and fixing of the schedule for its unearthing.