you'd have to check your state laws, as they vary. Depending on the car's value, DMV might let you sell on a Bill of Sale, but really, it's best for you and everyone to file for a duplicate title. If you file for a duplicate title, it can go directly to the new owner, and you're done!
If you never had a title on the car yourself, then you may be in legal difficulty trying to sell it to anyone.
I suppose you could sell it as a parts car only but if anyone tries to register it, it'll all come back on you.