The regulation cited by @dneran mentioned not issuing the 1099 form to a real estate agent or property manager. From the way you described it, I suspect the lessee is not a property manager or real estate agent, but rather a business owner that leased the property to you because they don't have use for it for some reason. That being the case, the safe thing to do would be to issue them the 1099 form.
The answer depends on to whom you are paying the rent, the property manager or the owner.
The IRS instructions for form 1099-MISC state:
Enter amounts of $600 or more for all types of rents, such as any of the following.
Real estate rentals paid for office space. However, you do not have to report these payments on Form 1099-MISC if you paid them to a real estate agent or property manager. But the real estate agent or property manager must use Form 1099-MISC to report the rent paid over to the property owner. See Regulations sections 1.6041-3(d) and 1.6041-1(e)(5), Example 5.
Thank you for the detailed response....just to clarify, I have a sub-lease that I pay directly to the original lessee of the building. So I would file 1099 for these payments, correct?
The regulation cited by @dneran mentioned not issuing the 1099 form to a real estate agent or property manager. From the way you described it, I suspect the lessee is not a property manager or real estate agent, but rather a business owner that leased the property to you because they don't have use for it for some reason. That being the case, the safe thing to do would be to issue them the 1099 form.