Yup, being pro-active is the best thing and I'd go within the company, even turning up in the department for an informal chat is good. Plus as you are in the "system" for the company they can more easily ask about you than being a faceless name on a piece of paper.
Plus you are showing you're a self-starter, a factor which a lot of people overlook as being important. You seem confident too, but also realise you have something to learn, so sound employable for me. If the manager wants you he'll find a way to get you in, it's nearly alway possible if the company is a good one.
The only thing *might* be that your agency has something in their contract with your employer giving them a bonus if you get employed full time as a result of their placement.
But overall, I'd take the bull by the horns and go after it, a lot of managers appreciate it when people are coming up wanting to work for them nd being honest with them - rather than grumbling in the background that they aren't being progressed even though the staff have never said a word.