They say it every year and they mean it. They don't want anything. They have enough. Don't spend money.
And every year somebody buys them a candle.
What they're actually saying
"I don't want anything" is nearly always shorthand for something more specific: I don't want more objects to look after. My house is full. I am at an age where things go out, not in.
That's a real preference and it's worth respecting rather than overriding. But it isn't the same as not wanting to be thought about. Those two get confused constantly, which is how people end up with a bathroom cabinet of unopened toiletries and a slight sense of not being seen.
The categories that survive it
Something consumable. Good coffee, the expensive butter, a box of the biscuits they'd never buy themselves. It gets used up, so it never becomes clutter. The main risk is that it's forgettable.
Something that replaces a worn-out thing. Not an addition — a replacement. The dressing gown that's gone thin. The reading lamp that was never bright enough. This requires you to have noticed something, which is most of the gift.
Something with your time in it. The lunch, the drive somewhere, the afternoon you actually turn up for. Reliably the best-received and reliably the one people don't do, because it costs the thing nobody has.
Something that asks them for something. This is the counter-intuitive one and it's the strongest. A book of questions for them to fill in. A photograph album with the first six pages already done and the rest waiting. Anything that says: I want what's in your head, and I've made it easy for you to give it to me.
People who insist they need nothing will often work quietly at that for months. It isn't a possession; it's a task with their name on it, which is a different thing entirely.
What to avoid
Anything that needs charging or an account. Anything that photographs better than it functions. Anything described as "a bit of fun" — that is the language of a gift bought in a hurry, and everyone can tell.
And be careful with nostalgia products aimed at older people. There's a lot of it about and much of it is condescending — the past served up as a theme rather than as something the person actually lived through. The test is whether it treats them as a source or as an audience.
The honest bit about giving
A gift for someone who wants nothing is not really about the object. It's a way of saying you paid attention. Which is why the expensive version of the wrong thing lands worse than the cheap version of the right one.
If you're stuck, the question isn't "what do they need". They've told you: nothing. The question is "what have I noticed about them this year that they don't know I noticed".
Answer that and the object mostly picks itself.