Cloe Wasey, manager of The Pigs in Edgefield, near Holt, Norfolk, said punters had been offering apples and marrows, mackerel and pheasants.
"If someone thinks it should be on our menu - and can produce it - we will do a deal," Metro.co.uk quoted her, as saying.
"We will consider anything edible - someone even brought in a deer which our chefs butchered for venison dishes," she added.
Customer Diana Rees, 44, from Cambridge, said: "I think it's a brilliant idea. You know what you are getting is really fresh and not out of a freezer - and it cuts down on food miles. We keep a few chickens, so next time I'll bring a couple of trays of eggs and do a deal."