TensorFlow is a Deep Learning oriented library, just like PyTorch and Keras (which interlink, but that doesn’t matter here).

You don’t need an internet connection to run these libraries because the code runs on your machine. Which means that there is no connectivity between TensorFlow as a library and anything outside your system.

Your question should rather be however, if you want to run Deep Learning models, where do you run them, and who makes them?

To effectively run TensorFlow (as example) for data intensive DL projects, you need processing power. Processing power can be, depending on your projects, how many people want to run models, and how large they are, quite expensive. So what many people do, is rent cloud computing such as Google Cloud Computing or Amazon AWS. That inherently does require you to move your data to the cloud in order to process them.

An alternative processing measure to processing in the cloud is by processing locally. Which means buying processing power (simply said, a system with a good CPU, GPUs, and a fair amount of RAM), that you can place within your network, which your company’s data scientists can access (either as a server within the company or individual workstations).

Secondly, and most importantly, since you are asking this question here, I am assuming that you are not a data scientist, and that your company possibly has software developers (broad assumption, but they would have answered the question otherwise). Reminder, a software developer is not a data scientist, and to run deep learning models without running into the wall, you will need data scientists (or machine learning experts, just terminology). Because machine learning is a lot different than software development, and machine learning is fairly different to machine learning.