Can you put an image on an NFC tag?
No, and two separate reasons each settle it. The smallest useful image is orders of magnitude larger than any tag capacity. And even if it fitted, no phone displays a picture handed to it by a tag, because nothing in the standard says it should.
The arithmetic
Tag capacity is measured in hundreds or a few thousands of bytes. A heavily compressed thumbnail is tens of thousands. A photograph from a phone camera is millions.
The gap is not one you close by buying a better chip. It is three or four orders of magnitude, and no tag on the market is within reach of it.
This is not a shortcoming. Tags were designed to carry an instruction, not a payload, and they are excellent at that.
The behaviour problem
Suppose the size problem vanished. The phone still would not show the picture.
A phone acts on a tag according to what the record says it contains. A web address opens, a phone number offers to dial, text is displayed. There is no defined behaviour for an image, so the operating system has nothing to do with one.
An application you write could read the bytes and render them, which means the picture only appears for people who installed your application. That is a much narrower deployment than a tag that works for everyone.
What people actually want
Usually one of three things, and none of them requires the image to be on the tag.
A picture shown after a tap, which is a web page containing an image. A visual that identifies the tag, which is printing on the tag itself rather than storage inside it. Or a logo in a contact card, which belongs on the page the card points to.
Naming which of the three you want makes the answer obvious in every case.
The pattern that delivers it
Write a short address to the tag. Put the image on the page. The visitor taps once and sees the picture, which is exactly the experience they asked for.
It also costs less: the tag can be the cheapest chip sold, the image can be as large as you like, and you can replace it without touching a single tag.
The only case this fails is a tap with no network, and an image is a poor candidate for offline delivery anyway. Where a tag must work offline, short text is what fits.
Frequently asked questions
What about a very small icon?
Even a tiny icon is thousands of bytes, and the phone still has no defined way to display it. Both obstacles apply at every size.
Can I print an image on the tag instead?
Yes, and that is often what people mean. Many tags accept printing on their face, which is a manufacturing option rather than a storage one.
Could my own app read an image from a tag?
It could, within the capacity limit, and it would work only for people who installed it. That is a closed system rather than a public deployment.
Does a bigger chip change this?
No. The gap between tag capacity and image size is measured in orders of magnitude, and no available chip closes it.