According to Steve Adams of MLBTradeRumors.com, Aardsma has a May 15 opt-out date on his current minor league deal.
Source: David Aardsma has a 5/15 opt-out date in his current deal with the #stlcards.
— Steve Adams (@Adams_Steve) May 7, 2014
Though his first 13 2/3 innings of work Aardsma holds a 1.98 ERA and 12 strikeouts at Triple-A Memphis. It would appear that Aardsma would exercise his opt-out if he is not called up.