CBI sources said the complaint has been received by them and it is being examined.
Singh, who had made the allegation in a media interview that forced Defence Minister A K Antony to order a CBI inquiry, had alleged in a letter to the agency on March 30 that there was a bribe offer from retired Lt Gen (Retd) Tejinder Singh, the sources said.
The agency had asked him to furnish a detailed complaint along with a possible witness list and other supporting documents so that they could proceed with the inquiry, they said.
Tejinder Singh has refuted the allegations and also filed a defamation case against the Army chief and other officers.
A preliminary enquiry or an FIR could be registered soon after completion of the procedural requirements, the sources said.
The Army Chief had claimed in media interviews that an equipment lobbyist had offered him a bribe of Rs 14 crore, a matter that he had reported to the Defence Minister.
The ministry had then recommended a CBI probe into the allegation made by the Army chief.