Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Zakah is not due on the building itself. It is due on the proceeds from the rent if they reach the Nisaab (minimum amount subject to Zakah) by themselves or gathered with other properties like money or trade goods, and if a lunar year passes after you possessed them. The Zakah then is 2.5%.
So, in your situation you are not required to give Zakah as long as you are not saving any amount liable to Zakah.
Allah knows best.