Based on the petition filed by retired police officer Jebamani Mohanraj, Justice K Venkataraman asked the Centre to reply within a week.
The petitioner alleged that Sinha was removed from a fodder scam case in a Patna High Court and he had not challenged the court findings of his "personal misconduct".
Manikandan Chettiar, counsel for petitioner, said an officer facing charges should not have been appointed as the head of the country's top investigating agency.
Additional Solicitor General P Wilson said the case had been filed based solely on newspaper reports.
Responding to it, Justice Venkataraman said media reports cannot be completely ignored and added the merits of the issue may be considered after getting the reply from the Centre.
Senior IPS officer Ranjit Sinha was recently appointed as the CBI director for a two-year term.
A controversy erupted over his appointment with BJP demanding that the Prime Minister keep it on hold, citing a recommendation by a Rajya Sabha panel on Lokpal that the selection be made by a collegium.
The government, however, said the selection of the 1974-batch IPS officer has been done in a "fair manner" following the "due process" and that the Prime Minister has got the authority to decide on one name.
