Jermaine Dye remains a member of the White Sox, and the possibility exists that he could stay in Chicago despite strong interest from Boston. The White Sox, according to an industry source, have made overtures about giving Dye an extension that wouldn't mortgage their long-term future. Dye can become a free agent after this season and seek a long-term extension elsewhere, even though he indicated last week that he wouldn't settle for a one-year contract. A big issue will be the monetary value of the deal, although general manager Kenny Williams may wait until the 4 p.m. New York (3 p.m. Chicago) deadline to see if another team makes an offer that tops Boston's.