What can we not know?
There are many things that humanity claims to know. We claim to know that 2+2=4, that a triangle has 3 sides, etc. We can go further, and claim that we know what happened a million years ago, or a billion, or even at the first few miliseconds of the Big Bang.
But what can we not know? Is there anything that humanity could not at least claim to know?
They've mostly been debunked.
So much people have claimed to see Jesus after questionably dying- and they described him as what you would describe every painting or depiction of Jesus.
But unfortunately, they are wrong.
The image of Jesus that you see now is not what Jesus looked like, it was just a depiction- a guess of what the painters during the renaissance thought he looked like. So the image you see of Jesus, is just an "Italian Man," because that's what they saw him as.
Of course, Jesus was born in the middle east, so the closest depiction of Jesus so far is a picture of what an average, primitive middle eastern man would look like, which looks far off in comparison to what we commonly believe he looks like.
The only way to express that knowledge of what is unknown, is to do just that. I'm sure there are many things that we do not know, and the only true unknown is that which we do not know that we do not know. If we can wonder about something that has no real answer, yet it is a question we can form in our minds, then there is already much speculation, and whether justified or not, we can claim that there are answers. We are one race of being, engineered/evolved a certain way, with a certain type of brain. I, personally, believe that there are more than likely many things about this vast universe that we cannot even begin to recognize or comprehend. That is what makes it unknown. To believe for even a moment that our minds have the ability to absorb all of the information that this world has to give us, is nothing short of ignorance fueled by undying egomania.
To deal with your question more directly, is there anything SPECIFICALLY that we cannot claim to know? Absolutely not, for as I've stated, anything that can be speculated, can be answered, or at the very least claimed as such. As far as what we do not know on the grounds of it being unknowable by us, I'd love to imagine that the possibilities are limitless, as with our one type of brain, it most definitely is.