I'd suspect he is not feeling right. You might try a vet checkup.
I suspect given his advanced age that he is loosing either his hearing or vision or both, this would cause him to be afraid and he's looking for you to be there for him more now than previously. If not one of his senses than yes something medically is going on. Please don't shut him away downstairs, he needs a good Vet exam including blood work. They are no different than we are as we age many illnesses conditions arise.
When our kitties have gotten over 15 - 16 years old, they have gotten more clingy. I think, as the other who responded, their senses are dulling so they look for comfort in a being they trust.
The semi-famous Miss Teia, who turned 21 in June, has become quite the lap kitty when I am on Her Couch.
You may also notice kitty does not have as large a range in the house.
He is in the twilight of his life, love on him.