The apex court also allowed Sundar Raman to continue as chief operating officer of the seventh edition of Indian Premier League.
A bench headed by Justice A K Patnaik, however, expressed reservation over ordering a SIT or CBI probe, saying that institutional autonomy of the Board has to be maintained and a committee constituted by the BCCI to look into the issue would be preferred.
"Having come to know the nature of allegations, we cannot close our eyes," the bench said, adding that it is concerned about the game of cricket in the country and not about individuals.
Referring to a sealed envelope report of Justice Mudgal committee, the bench said, "It (report) said all these allegations were brought to his (Srinivasan) notice but he did not take any action. That means he was aware about the allegations and did not take it seriously."
In the meantime, the bench allowed Raman to continue to function as Chief Operating Officer (COO) of IPL 7, which is to begin today in Abu Dhabi.
The bench allowed his continuation on the post after veteran cricketer Sunil Gavaskar, appointed as an interim president of BCCI by the apex court, has written to it to take a decision on the fate of Raman.
The apex court had earlier asked Gavaskar to take a decision on whether to remove Raman as COO or not.
The court also made it clear that IPL 7 would go on, as scheduled, and it also agreed to hear the plea of BCCI and Srinivasan for allowing them to get the tapes of audio recording of interactions of the Mudgal committee with Indian captain Mahendra Singh Dhoni and Srinivasan.
Srinivasan had yesterday knocked the doors of the apex court for reconsidering its interim order keeping him away from the affairs of the Board and sought its permission to resume his office, the tenure of which is till September this year.
Srinivasan, who narrated the sequences of events that led the apex court to ask him to discontinue functioning as BCCI president, had contended that "unfair and unsubstantiated allegations" were made against him by the senior counsel appearing for Bihar Cricket Association (BCA).
In an affidavit, he had claimed that he never interfered with disciplinary proceedings or criminal investigation against his son-in-law Gurunath Meiyappan, who is one of the accused in IPL spot fixing.
Responding to the allegations levelled by the BCA and adverse remarks made by the apex court, Srinivasan, who is the Chairman of the India Cements, the owner of Chennai Super Kings, had said he never made any offer to step aside as the Board President and a proposal in this regard was given by the BCCI on March 27.
He had also denied allegation of senior advocate Harish Salve that he was guilty of corruption and "cover up" and also expressed his ignorance that the sealed envelope submitted by the Mudgal Committee contains any audio tapes having conversation between two accused of betting -- Vindoo Dara Singh and Meiyappan.