Eugene Gendlin is the discover/creator of focusing. He calls the thoughts/feelings that focusing works on "felt senses".
The primary book he wrote on this is Focusing. This excellent book, which you should buy, lays out his ideas and is a wealth of good examples.
Gendlin's contribution to focusing, and hence to psychology, is enormous. Yet his is not the last word on focusing; his followers have made further contributions. Gendlin nonetheless seems to have laid down the complete basic process in his first book. On the website, the "normal" focusing pretty much follows Gendlin's basic procedure.
In this book, Gendlin say the "felt senses" are in the body. The body is not built to store information, especially the complex information in a felt sense. The brain is built to store information and to think. So the brain is the logical location for felt senses. (And even if the body could store that information, that information would need to be transmitted to the brain for it to become a conscious experience.)
Of course, it might be useful to think of a felt sense as being in the body, just as it is useful to think of the felt sense as being a person you can talk to.
More generally, this website takes its own approach to focusing and "felt senses".
Another excellent book, which has influenced the focusing on this website, is The Power of Focusing: A Practical Guide to Emotional Self-Healing, by Ann Weiser Cornell.