If you mean your mortgage on the rental property, you will have no choice but to pay it off. Mortgages are due in full on sale.

It is hard to tell what you mean. If you have a purchase and sale contract, that stipulates that the buyer is to take the property free and clear of any encumbrances, and use an escrow, then the loan will be paid off as part of closing. The result is different if you transfer to someone without using an escrow or the stipulation that they take the property free of encumbrances. In that situation, the property would still be subject to the deed of trust.

Do you mean the mortgage on the rental property that you are selling, or the mortgage on your own house?

Normally, when someone sells a piece of real property, the existing loans are paid off out of the sale proceeds, before the owner gets a dime. Occasionally, a lender will allow the buyer to assume the loan, which remains in place with a new borrower substituted for (or added to) the original borrower. I think such loan assumptions have become less common lately, at least in part because interest rates on new loans have dropped so low.

So, one possible answer to your question is not only can you, but also, you probably MUST pay off your loan ---- if we're talking about a loan on the property being sold.

If, on the other hand, you mean a loan on some other property, such as your principal residence, the answer would have to be "it depends." Among the things it depends upon is how much cash you get from the sale vs. how big your outstanding balance is.

You can always pay off a mortgage if you have the money. It doesn't matter where it comes from, either sale of the property, or sale of some other property, etc.