A method and apparatus are provided for processing a request to instigate communication, received by a routing device associated with a plurality of terminals. The request relates to a communication to be established between a sender device of the request and at least one of the terminals. The method includes a step of comparing communication capabilities of said sender device with respective communication capabilities of one or more terminals, called addressee terminals, which are able to establish said communication, so as to identify at least one terminal having capabilities making it possible to establish with the sender device a communication of maximum quality. A call notification is transmitted to at least one of the addressee terminals, which is suitable for triggering on the addressee terminal a call presentation prompting a user to use, by priority, one of the terminals identified during the comparison step to establish the communication.