As an ethical issue for the auditor, “conflict of interest” means between a client and the auditor – NOT between different clients. There is nothing “wrong” with having client who are competitors (in fact, some audit firms develop expertise in particular industries – hotels, for example – which means that they have lots of clients who compete with one another). In this scenario, the ethical threat is breach of confidentiality (intentional or unintentional), for which the safeguard would be separate audit teams.
See page 27 of our notes describes how one client making a bid for another client would create a conflict of interest.