When a serving of food has less than 200 mg of potassium, it is considered a poor source of potassium. This includes berries like strawberries and blueberries, cranberry, other fruits such as apples, pineapples, and grapefruits. Vegetables with low potassium content include cauliflower, broccoli, eggplants, and green beans. White rice, white bread, and pasta are also poor sources of potassium.