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The Angels have an offensive future on the horizon, but they do not have any young pitching beyond Tyler Chatwood. Kendry Morales will return to the lineup for the Angels next year and so will world-beating prospect Mike Trout.
If the Angels trade away one of these guys, they are jeopardizing the future of this team for years to come. The best pitcher this off-season, assuming Sabathia returns to the Yankees, will be Mark Buerhle. The Angels have no way, or no reason, to replace Weaver or Haren.
Moreover, they may be able to add Prince Fielder or Albert Pujols in addition to Trout and Morales next year, and they could also add offense by trading Ervin Santana, as opposed to Haren or Weaver.
This rumor does not pass the smell test.