IF, you're the holder of the note and the borrower is not paying the mortgage, that's an entirely different situation.
However, noting that your question appears in the "Foreclosure" area. So I'm guessing you owe money to a bank. You have a mortgage. And you're trying to find a way out.
In that case, you wouldn't sell the mortgage to the bank. It's the bank's mortgage.
If it's similar to what Cori guessed, my response is a bit different than hers.
If you're considering having someone take over your mortgage payments, yes, that can be done. That's called a "subject to" transaction--they're buying your house "subject to" the existing financing. That means ownership would be transferred to the individual, but you would still be responsible for the mortgage. They'll promise that they will pay the mortgage...and they probably will. But you have to understand that, if they fail to, the bank will come after you, not them. The mortgage is still in your name.
Such a transaction violates the "due on sale" clause in your mortgage. But that's not against the law, and it's done frequently.
The other scenario Cori suggested was that the individual would be your new lender. That, too, is possible. But watch out for promises of a sale and leaseback with an option to repurchase. Some are legitimate; some are not. Most legitimate investors don't do that anymore. That involves someone approaching you and saying, "I'd like to buy your house. You can continue living in it. You'll make your payments to me. After a year, I'll sell the house back to you." A couple of questions: If you're having trouble paying your current mortgage, why will it be any easier when you're paying off a larger loan to someone else? And after a year or two, even if you do struggle by and make the payments on time, will you be financially able to repurchase your house? Probably not.
So, be careful.
The answer depends what you are trying to do.
If you are trying to have them take over your mortgage payments. It can be done if your lender allows assumption of your mortgage. Your lender can tell you if your loan allows this.
If you are trying to have this individual be your new lender. This can be done by having them payoff your existing loan. You can then make payments to this individual instead of your bank.
Please fell free to call me directly if you have any questions,631-944-8829.