The inmates, named as Nishant and Amit, alleged they were given a knife and a pistol by prison officers to kill the Games officials who are themselves being held on corruption charges.
Three senior Delhi Commonwealth Games officials - TS Darbari, M Jeyachandran and Sanjay Mohindroo - are in custody at the same jail having been charged with financial irregularities leading up to the October Games.
The chief metropolitan magistrate, Vinod Yadav, had ordered a police investigation into the matter and asked for a report by Friday but the deadline was missed.
"The court itself will now enquire into it," he was quoted as saying by the Press Trust of India news agency after police failed to complete the probe in the stipulated time frame.
"It is a fact that a knife has been recovered from the jail and the matter needs to be taken seriously."
The $6 billion (£3.9bn) Games was intended to showcase India's growing financial might but threatened to become a farce and only late scrambling by the government salvaged the event.
Central Bureau of Investigation officials on Friday raided the homes of Suresh Kalmadi, chief organiser of the Games, as part of the investigation into the alleged financial irregularities related to the staging of the event.