The bench said that the court cannot interfere in all sensational matters and there should be a basis to pass an order which cannot be done merely on the ground of assumption.
The court was hearing the PIL filed by advocate M L Sharma seeking directions for ensuring proper arrangements for safety and protection were made at the site so that any hidden treasure should not get into wrong hands.
The bench said that no order was required at this stage.
The petitioner had submitted that court monitoring was required in the case as "the valuable resources might vanish".
The court had on October 18 said that the state government was there to take care of the process and had agreed to hear the PIL only after the defects were removed in the petition.
The much-hyped excavation is being carried out by the ASI after a seer, Shobhan Sarkar, dreamt that 1,000 tonnes of gold were buried in the fort of Raja Rao Ram Bux Singh, a 1857 revolt martyr, in Daundia Khera village.
Sarkar has claimed that treasures were also hidden at many other places in UP.
His claim was not taken seriously by the local administration and the state government.
However, a Union Minister later visited the area and met Sarkar. The minister then directed ASI to work on it, which began on October 18.