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There are no Kolping houses in Leipzig, and hardly any in eastern Germany as such. You will have to find an alternative.
The biggest student accomodation in Leipzig is organized by the University, but you need to prove that you are studying in Leipzig before you get a room there.
Another solution is the "Evangelische Studienhaus" which is however strongly religious (reformed) and they are not really clear if you need to be a student to live there.
You best bet might be one called Youniq, which is more of an independent company running student homes (also as a investment opportunity). They operate 3 houses in Leipzig, and do so also for non-students, with a special FAQ for those and the whole website is available in English.