Should I mention in my statement of purpose that I am applying because of my girlfriend I am applying to a university for a PhD position because my girlfriend is a PhD student there. Our affair is quite serious and it is almost surely going to convert into a marriage. We might even get engaged in 2019.

I have been in touch with professors from this university. Moreover, I am using some of the results of another professor directly in my masters thesis. I have a lot to write in the statement of purpose from a technical point of view.

However, because of my girlfriend, this university becomes a top-priority for me against all other PhD offers I may get and I want to stress this in my PhD application.

Should I mention this in my SOP? How should I mention it, if the answer is yes.
I can't see any scenario in which that would help and can see many in which it would hurt you. The first question asked would be "Is this guy serious???" People are looking for people dedicated to the academic process, research, learning, etc. Personal reasons such as this, and many others, shouldn't be mentioned. Take about why it is that you want to work with this faculty and what  your long term academic goals are.