I think you're not quite using the right terminology. Specifically, you'd "sell" a mortgage if you'd been the owner, took back financing yourself, were holding the mortgage, then wanted to sell it for a lump sum, rathre than receive monthly payments. The answer then would be yes. It's done all the time.
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.