As long as you own the property and the monthly mortgage payments continue to be made on time you can enter into a rent-to-own agreement for someone to buy the property, even though you are not on the mortgage. In short, unless the mortgage documents contain specific provisions that do not allow the property owner to rent out the property or establish a rent-to-own arrangement, then you can freely enter into these agreements.
Please note that if the borrower indicated on the mortgage application that he or she intended to live in the property (which qualifies the borrower for an owner occupied mortgage), then the borrower is typically required to occupy the property for at least a year after the loan closes, absent a job relocation or other significant life change. As long as you are more than a year removed from mortgage closing, then the borrower can move out of the property and rent it out or do a rent-to-own with a new occupant.
It is important to highlight that the lender is primarily focused on the borrower paying the mortgage on time. As long as the lender receives its monthly payment, then what the property owner decides to do with the property is of secondary concern as long as the owner and borrower abide by the terms of the mortgage.
Another issue to keep in mind is that when the ownership of a property is transferred from one person to another, it may trigger an acceleration clause in the mortgage which requires the borrower to repay the outstanding mortgage balance in full. For example, when you sell a property, ownership changes and you are required to payoff the mortgage. This is usually not an issue because you can use the proceeds from the sale of the property to payoff the mortgage.
If the acceleration clause is triggered without selling the property, if you or the mortgage borrower cannot payoff the outstanding loan balance it could cause the lender to foreclose on the property. This means you could lose the property and the borrower would have a foreclosure on her or his credit report.
The acceleration clause is not an issue when you rent out a property because the ownership does not change. The clause should also not be triggered if you enter into a rent-to-own agreement because the individual who moves into the property rents and ownership of the property is not transferred until the completion of the agreement, at which point you would likely be required to payoff the outstanding mortgage balance.
Although you are not listed as a borrower on the mortgage, I recommend that you review the mortgage note to understand if the acceleration clause is applicable to your situation. With this information, you should be able to structure a rental or rent-to-own agreement that works for both you, the property owner, and the borrower.