Lieutenant Governor Winthrop ockefeller says the chances are remote that he`ll seek the Republican nomination for U.S. Senate next year. Democratic Senator Blanche Lincoln is up for re-election in 2004. Governor Huckabee, a Republican, this week announced that he would not run. Rockefeller said Wednesday he`s not interested in running and he reiterated that Thursday. Rockefeller, the billionaire son of former Republican Governor Winthrop Rockefeller, and his wife have eight children, five still in school.