Alma 37:4 states the following:
"Behold, it has been prophesied by our fathers, that they [the plates of brass] should be kept and handed down from one generation to another, and be kept and preserved by the hand of the Lord until they should go forth unto every nation, kindred, tongue, and people, that they shall know of the mysteries contained thereon."
According to David Palmer, this is an explicit prophecy by Alma that the brass plates would be published to the world some day. Of course this would probably necessitate that the record sanctuary where it was eventually stored by Mormon would someday be discovered. [David A. Palmer, In Search of Cumorah, p. 218]