First, I'd sit down with your project manager and any other technical management you have and clarify expectations. You don't want to cause confusion if you get more agressive, and you don't want the project manager to be out of the loop. I think it's safe to start with stating your own expectations that you would be taking on this sort of work, providing in house expertise, but that the biggest questions are how and when should you begin taking control?
For example - are you expected to start doing the work yourself on this project? Or do they have in mind that you take control on the next project? When do they want to sever the relationship with external contractors? And what assurances does management need before they feel comfortable with you taking control?
I think you want answers to this, and if the project manager and any direct technical manager that you have don't know, you have to keep asking up the management chain until you get someone responsible for this strategy.
It's usually my style to pull everyone into a final clarifying conversation, because I dislike cases where communication gets muddied in multiple transmissions. It can be conference call, in person or email - but something where all stakeholders are privy to the same rendition of the same information is vital here.
In many cases, you are asked to work side by side with the redundant team because it is expected that you will learn how assignments and comunication flows, and what your responsibilities will be. It's worth it to keep track of how work gets done and to ask plenty of questions so that, at least at first, you'd be comfortable emulating the other group's process as much as possible.
In the long term, you may put your own spin on how the work gets done... but before you can do it successfully, you need a sense of the scope of it, and the expectations.
If there isn't a written plan of how the work you are taking over will be transferred to you, a place to start may be drafting thoughts on this. It'll let you make sure you are on the same page, and let management step in to redirect you if you have gone off course.
Be careful with information
Be very careful with the outside contractors until you know the lay of the land. Unfortunately, it is likely that they trust that they will always be doing this work for your company, and that trust is likely to get messed up when it comes out that you are there to replace them.
They may still be part of your company's strategy, they may not be - either way, let management roll out this information. For the moment, remain a helpful collaborator who asks thoughtful, reasonable questions, and who reviews the work and provides internal team expertise as you can.
It's a tough trick, communication wise - you certainly don't want to lie to the external team, but you do have to be aggressive enough to start learning how they do the work and how you may take it on.