Does my supervisor want me to do my Ph.D. with him or elsewhere?
As Peter said in his comment, ask him.

However, having said that, and based on what you have said, it is very clear that he is not 'kicking you out' at all - on the contrary, he is demonstrating a very positive and constructive approach - by telling you that you have to pursue what is best for you.

Having said that, you need to consider a key question:


What is/are your goal(s) after you complete your research?  


The professor is, as you say not an expert in the field you are interested in, and what he is suggesting is that, as this is the case then the internship may lead to opportunities that are more in line for your plans.

He is also seemingly suggesting is to pursue the internship and then decide where and what you want to study for your PhD.

Ultimately, the decision is yours to make - he is helping you to help yourself in this regards.

But, a piece of advice, do not assume to know the intentions of anyone - take his advice on face value and in the spirit that it has been given.