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.
If you mean that you would borrow Zakah money that is due now which a person has not yet paid off to its recipients, then this is not permissible because Zakah is the right of its eligible people (i.e. recipients) and it must immediately be paid to them. A person who is obliged to pay Zakah is not permitted to act with it as he wishes, by lending it to others and the like, because he does not own it and he is obliged to pay it to its eligible recipients.
However, if you mean to borrow money from Zakah money after it was paid to its legitimate recipients, then this is permissible because by paying the Zakah to its legitimate recipients it becomes their property and they may dispose of it as they wish, by lending it and the like.
For more benefit on the recipients of Zakah, please refer to Fatwa 88368.
Allaah Knows best.