It is possible this could be a sign of a problem. Older cats are prone to certain conditions that affect the appetite. Hyperthyroidism is a common one. In this condition, the thyroid gland is overactive (usually due to a benign tumor), and secretes excess hormone. This increases metabolism and also increased hunger. The cats typically lose weight even though they eat a lot, and they are always hungry. Your vet can check for this with a simple blood test called the T4 level.

Diabetes is another concern in older cats. There are usually other symptoms as well as appetite changes, such as increased thirst and increased urinations. They will also lose weight.

The best thing to do for your cat right now, in order to determine if there is a problem or not, is to take him to the vet for a check up and blood screen. That way you will know if he is just being a pest, or if there is a medical problem causing these symptoms. Treatment can be discussed once a diagnosis is made.

Please reply if you have more questions!