The agency had received a complaint from the Defence Ministry to look into the supply of aircraft engines to HAL and is scrutinising the documents, highly placed sources said.
Defence Minister A K Antony has ordered a CBI probe into the allegations.
They said a preliminary enquiry may be initiated by Wednesday on the basis of which a decision could be taken to register the FIRs in the cases.
"We will co-operate fully with the regulatory authorities and have repeatedly made clear that we will not tolerate misconduct of any sort," a Rolls-Royce spokesman has said.
Sources said the role of a London-based arms dealer, who had been probed by the agency in different cases, is also under scanner and if evidence of his role emerges, he might be made an accused in the FIRs.
They said the arms dealer who is already in the list of "undesirable contact" issued by the agency to government officials has been probed in the past but since no evidence
had emerged the cases were closed.
The scandal relates to deal in the supply of engines for Hawk trainer and Jaguar fighter aircraft between 2007 and 2011 and an internal probe by the vigilance wing of HAL has prima facie established the charges, the sources said.
The allegations surfaced in the form of a letter received by HAL recently claiming that bribes were paid to officials in HAL and other departments concerned to bag contracts.