Do cats talk? Of course they do. It's just not always with their voices. Our cat's "native language" is body language.
If we have more than one cat, they will speak to each other with the shape of their eyes, the flickers of their ears, or a quick shoulder bump when they pass in doorways. Cats try talking to us with these same gestures. If we pay attention, we can see them "saying" things to us.
But cats are also capable of understanding what we are saying with our words. Not enough to write a human-to-cat dictionary, perhaps, but they certainly grasp the meaning of words like "dinner," "playtime," or "cuddle." What helps our communication is talking to our cats. We can't help but display our own body language along with our verbal language.
For cats, it's like we are sub-titled.
So while our cats might make verbal requests, they are always making body ones. Staring into our eyes, getting in our way when we get up, and laying a paw on our arm are all ways our cat asks for things.
Whether they "say" anything, or not.
For more about cat communication, see Cats asking questions.