The LA Times says yes:
The Angels ... resumed their pursuit of Chicago White Sox first baseman Paul Konerko, who turned down a five-year, $62-million free-agent offer from the Angels after 2005 to remain in Chicago. According to several industry sources, the Angels, looking to add a power bat to their sagging offense, have inquired about Konerko, who is batting .261 with 22 home runs and 61 runs batted in. Konerko has a limited no-trade clause and is signed through 2010, but he has a good relationship with Scioscia and would probably waive the clause to come to Anaheim. But the White Sox, who are 14 1/2 games back in the American League Central and are in a selling mode, haven't decided whether to trade Konerko or right fielder Jermaine Dye, who can become a free agent at the end of this year. The Sox have made it clear they don't plan to tear down the team and don't want to completely strip their lineup. They are shopping pitcher Jose Contreras but are getting more inquires about pitchers Jon Garland and Javier Vazquez, all of whom could be of interest to the Angels.
I say NO
. We're not looking to destroy (tear down) the team.
BTW, Cowley says:
The two leading candidates for the Sox to move remain right-handed pitcher Jose Contreras and outfielder Jermaine Dye. The leading suitors for Dye are the New York Mets, San Diego Padres, Los Angeles Dodgers and Seattle Mariners. The Mets and Mariners also are scouting Contreras and will have one more chance to do so tonight against the Detroit Tigers.