The problem is the potential buyers of the paper- banks, insurance companies, etc all want listed papers. Thus the question should be can a private company get its NCD's listed?
I personally feel yes, there is nothing in law that prohibits it. NSE feels (at least felt some four years back when I had taken up a client's case) NO. BSE agreed in principle that private companies can get their NCDs listed but it is very choosy in giving that in-principle approval. Their logic is simple. Listing agreements call for certain periodic disclosure statements. Public companies are legally bound to make those disclosures. Private companies have no such legal binding. If after listing of the NCD the issuer does not make periodic disclosures to the exchange all that can be done is delist the paper.