Applying for Post Doc position with already one in hand I have finished my PhD in Germany recently and am applying for post doc positions here. I have an offer from one branch of a reputed research organization among the other institutes of the same organization that I applied to. 

The people at the institute have initiated the process of processing the contract. Although I like the work that they are doing, I am looking for replies from other institutes since they are in a location that is preferred by me.

I am now in a fix that if they have already initiated the process, would I be able to attend interviews by the other institutes of this organization or does the hiring process reflect in the database and would I not be called for any more interviews at all.

If it helps, the organization is of the likes of Fraunhofer, MPI, Leibniz institutes.
Typically different institutes, even within the same organization (e.g. the Max-Planck or Fraunhofer group), don't formally exchange information on applicants to their positions, so you don't need to be afraid that they won't consider your application just because you're in the process of getting hired somewhere else. However, you shouldn't underestimate informal information exchange - if you're in a small field, the PIs who want to employ you may well talk with others about that post-doc they are going to hire soon.

Moreover, if you've already explicitly agreed to an offer at one place, and they are preparing the contract, it perceived as very impolite to back out of that. Legally, it's still possible to do, and if it makes a really big difference for you, then you should probably do it, but be prepared that it will annoy the person you agreed to working for.