If you want something like SignalR then why would you not just use SignalR? Maybe you don't actually want something like that at all.
I suspect that what you want is a Web API, which is basically an MVC app without the V. You create an ASP.NET application project the same way but, instead of MVC, you choose Web API. You then create a model and controllers in basically the same way but, instead of views, your controller actions return data, often as JSON. Anything with web access can then connect to your API, including an MVC app. Where you might otherwise create your service layer as part of an MVC app, you can create it as a Web API instead, then have both the MVC app and other applications, e.g. mobile apps, connect to that common service for their data.