Enterprise Service Buses (ESBs) constitute a core middleware technology for each modern Service-Oriented Architecture (SOA) solution. Given the popularity of the Cloud paradigm, which is based on fundamental SOA concepts, it is only therefore natural to look into how ESBs can be transformed into native building blocks for Cloud platforms. As a first step of this effort, in this work we investigate how ESBs can become multi-tenant aware, i.e. able to support multiple tenants and their users sharing the same ESB instance. A generalized architecture based on the JBI specification implemented by a number of open source ESBs is presented for this purpose. We demonstrate the feasibility of our proposal by means of a proof of concept realization and we evaluate the performance of our solution against a non multi-tenant ESB that was used as the baseline for our implementation.