Sinha said he was ready to recuse himself from the investigations if the apex court wanted him to do so.
Bhushan had earlier filed a similar plea to keep Sinha away from the 2G spectrum investigations.
A Bench headed by Chief Justice RM Lodha is likely to hear Bhushans fresh application on Tuesday.
Bhushan's demand is based on visitors diary maintained at the CBI chief's residence. The entries reportedly showed that Sinha met representatives of Reliance Telecom, a company being investigated in the telecom scam, and Rajya Sabha MP Vijay Darda and his son Devendra Darda, who were being investigated in a case of illegal allocation of coal block.
Besides, Sinha also met Subodh Kant Sahay, former Union minister, whose brothers company is one of the beneficiaries of the allocation of coal blocks and is being investigated by the CBI, the activist lawyer said.
Sinhas frequent meetings at his residence with the accused in prominent cases like coal block allocation scam and 2G scam are the attempts to damage the CBIs case in 2G cases, for which he was strongly criticised by then senior public prosecutor UU Lalit, the application stated.
Sinha said: I will recuse myself if the court wants me to. The apex court is hearing the matter related to the 2G case and a petition in coal scam has also been filed in connection to my supervision. I have done no wrong in the trial and investigations of both the 2G and coal scams, he said.
Filing the application for Common Cause, an NGO, in the coal scam, Bhushan said the CBI directors role in the investigation deserves scrutiny as he had last year unauthorisedly shared coal scam status probe report" (meant to be confidential for the court) with the then UPA government.
He also alleged the CBI director and senior officers forced investigating officers to file closure reports in cases where FIRs have been filed in coal scam cases. Last week, the Supreme Court had declared that all 218 coal block allocations since 1993 are illegal. It has not yet decided whether to cancel the licenses en masse.