If I follow you well, you search a way to listen some request through your client? So you want your client to be a server.
I don’t know any plugins that allow your client to came a HTTP server, if you want to do this, you’ll need to build your own TCP/UDP protocol inside ue4, if you never heard about network programming, you should start searching for TCP/UDP server.
they are some good example of HTTP server out here. Maybe you could implement your own inside unreal, but honestly I wont recommend you to do this, I personally prefer to have my server on another machine and let client send request to himself and if I need to talk to specific client, they are always listen to what we call a «socket».
But anyway let me know if this help you and please let me know why you need to have a server inside unreal for a website.