In the book that I read it says that A. Malcev gave such an example in 1936. But I can't find it... any help will be appriciated.
Searching for "cannot be embedded in a division ring" with Malcev's name yielded this article, which cites the example on the final page.
Malcev, A. L. "On the immersion of an algebraic ring into a field." Mathematische Annalen 113.1 (1937): 686-691.