As Helen says, and while I don't want to disparage your agent before you work with them at all, it is a little odd for someone to ask you to perform a monologue for screen...because it's almost a contradiction in terms! The last thing most actors ever have to perform on screen is a monologue! And that's why you'll find it hard to track down monologues in screenplays, as opposed to stage works.
Giving the benefit of the doubt, I'll assume that your agent still knows what they are looking for - and they are asking to see you perform something of a decent duration, but to try and assess the quality of potential screen performance from it, because they are primarily interested in selling you for screen work. Which I suppose is fair enough. The (slight) difficulty you have is knowing whether or not they can *actually* appreciate the difference between a stage performance and a screen one!
That sounds ridiculous - but, in actual fact, some of what has to be done to convey a good screen performance will not read at all well if a camera is not trained at you at the time, recording what you do for playback later. Your best bet may be to find a 'middle path' between stage and screen performance for the sake of showing what you can do here.
Essentially, the things to remember about screen performance are that while it is contained, it does not lack emotional engagement. This means that, in effect, you need to be as emotionally connected to the material as you would be in a stage performance, but you should work as if you were in close up shot. There is no point in needlessly moving around the room, because this would distract the camera in the real situation. You do not need to project loudly, merely speak loudly enough to be heard by a microphone that is about 12 inches away from you. And the reactions on your face are as important as what you say. These are actually the real 'secrets' of good screen acting.
What is uncertain here is that, if you are not actually being recorded on camera (I assume you won't be), how *really* working like an experienced screen performer will come across. You may, if you're not careful, end up too quiet to be heard (this doesn't matter when you are speaking into a mic, and some of the best screen actors in the world use incredibly low levels of voice), and exagerrated reactions may look odd when you are simply addressing a person sitting across from you in the room, rather than playing for the lens. The best option for the circumstances I think is, therefore, to lower your vocal levels a little, pare down your movement, keep your focus intent, and try, if you can, to keep your head up from the page you are reading from as much as possible (if you can learn the monologue, so much the better). This is not quite everything you'd do in a screen performance, but it will give the impression that you know the difference between this, and the sort of bold gesticulation and articulation that is demanded on stage.
If you are asked to work for a camera, then, by all means, go for it as if were a screen test, and knock their socks off with your skill - but I wouldn't have thought an agent would go to those lengths.
