Cubs president of baseball operations Theo Epstein said calls have picked up as the Deadline approaches.
"You can express a preference for pitching," Epstein said, "but if we're dealing with a club that has better position player prospects or we feel position players in a certain system are a safer bet or offer a higher upside, I don't think it's fair to pigeon hole yourself to one situation.
"As a whole, not specifically regarding these potential deals that are upcoming, we need to add a lot of pitching to the system. It's not enough to have a handful. We need to have waves and waves coming into the system. We don't have that. We hardly have one wave. We need to build a lot of pitching depth."
Dempster, who will be a free agent at the end of the season, is reportedly drawing interest from several teams, including the Dodgers. He has 10 years in the Major Leagues and five with one team, so he can veto any deal. Epstein would not reveal which teams Dempster favored.
Garza, on the other hand, would be under a team's control through 2013. Right now, the Cubs are looking to the future.
"It's an opportunity," Epstein said of the Trade Deadline. "We want to make the most of it. We wish we were looking to add, and hopefully in the years going forward, we'll play better in the first three, four months of the season and be in a position to add going into the playoffs."