The obvious answer is no. The definition of market rent is: “The amount the owner could charge and obtain for the lease of a property in the current economic circumstances.” Why would anyone take less income and reduce the value of their property?

On the other hand, there are owners who have tax issues if they sell, are afraid of a vacancy, or need the income and don’t want to concern themselves with vacant space and the issue of leasing. These owners are called amateurs. Giving money away is a worthwhile trait. But it should be given to a worthwhile cause and not to the lessee(s) and future buyer of the property.