All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
What is paid in advance in return for rent becomes the property of the landlord, and it is obligatory for him to pay the Zakah for it. The landlord should pay Zakah for that money and not the tenant because once he pays that sum of money to the landlord and it is transferred to the possession of the latter, it becomes his own property [and Zakah is required for it if it reaches or exceeds the Nisaab].
Ibn Qudaamah wrote, “If the landlord leases the house for two years for forty Dinars and the lessee pays the rent upon the conclusion of the lease contract and it is transferred into his possession, then he (the landlord) is obliged to pay Zakah for that money after the passage of one lunar year of possessing it because it has become his property and he has gained the right to dispose of it in all ways.” [Al-Mughni]
Allaah Knows best.