Is this library by Mark Seemann the answer? In the description he writes explicitly :
This approach enables the use of Dependency Injection (DI) because the
request can be injected into the services which require it.
Then gives an example :
// Inside an ApiController
var uri = this.Url.GetLink(a=> a.GetById(1337));
By which you can then pass the URL down the road in the service that you have injected in the controller.
UPDATE :
Mark Seemann wrote about the same exact problem here:
"Because HttpRequestMessage provides the context you may need to
compose dependency graphs, the best extensibility point is the
extensibility point which provides an HttpRequestMessage every time a
graph should be composed. This extensibility point is the
IHttpControllerActivator interface:..."
This way you can pass request context information to a component deep in the object graph by getting from the HttpRequestMessage and passing it to the DI container.
Just take a look at the interface of IHttpControllerActivator.
The WEB API framework gets the IHttpControllerActivator through DependencyResolver. You probably already replaced it by your CastleWindsorDependencyResolver. Now you have to implement and register your HttpControllerActivator and register it.
When the WEB API framework gets IHttpControllerActivator from DependencyResolver (your Castle Windsor DR) and calls IHttpControllerActivator.Create() it will pass you the HttpRequestMessage. You can get your info from there and pass it to the your CastleDR before you call Resolve(typeof(MyController)) which will resolve the whole object graph - that means you will have MyHttpContextInfo to inject in your XYZComponent deep in the resolution stack.
This way tou are passing the arguments in the last possible moment but it is still possible. In Castle Windsor I make such passing of arguments though CreationContext.AdditionalArguments["myArgument"];.