Dempster has not yet exercised this right. In fact, there is still a chance he could end up with the Braves. But for now, the veteran pitcher plans to spend a few more days thinking about his options.
"It was an opportunity to get one of the premium arms in this Trade Deadline market and arguably the guy that is pitching the best in baseball," Braves general manager Frank Wren said. "That's the positive side. The negative side is that it hasn't gone through as quickly as we would have liked."
Wren was quite busy on Tuesday, as a handful of teams called to talk to him about trades that would bring a starting pitcher to Atlanta.
Wren was not willing to trade any of his top pitching prospects -- Delgado, Julio Teheran, Mike Minor or Arodys Vizcaino -- last year. Since the details of this proposed trade with the Cubs became public, it appears teams are now showing more interest in talking potential deals with the Braves.
"If this deal materializes, we have the framework of a deal with the Chicago Cubs," Wren said. "If it doesn't, then if something else were to present itself, then they know we are going to move on to other things."
Dempster has told reporters over the past few weeks that his first preference would be to play for the Dodgers, where he would be reunited with his best friend and former Cubs teammate Ted Lilly.
The Dodgers were unable to reach an agreement when they discussed the potential to acquire Dempster earlier this month. They appear to be more interested in Cubs right-hander Matt Garza.
"I'm just trying to look over everything and make the best decision for me and for my family and what I need to do," Dempster said while adding that he might wait until next Tuesday's Trade Deadline to make a decision.
When the Cubs were playing at Turner Field earlier this month, the Braves gained indication he wanted to play in Atlanta. If the deal does materialize, this wait will not influence the way Chipper Jones and the other Braves welcome the likeable pitcher to their clubhouse.
"I'm sure when you've been in one spot for a really long time, being traded is a big adjustment and there is more than just the business of baseball at hand," Jones said. "You've earned the right as a 10-and-5 guy to choose where you go. Family becomes a big part of the decision-making process."
As for reports that he was blindsided by the deal, Dempster said the Cubs' front office has kept him up to date on everything. He didn't expect it to be made public.
"I haven't made any decisions on anything," Dempster said. "I'm looking at everything and trying to explore every option and do what's best for me."
Dempster was not willing to comment on the proposed trade when it became public on Monday afternoon before he had decided whether to provide his approval.
"The unfortunate part is that it got public," Braves general manager Frank Wren said. "These things happen. But when players have no-trade [clauses], whether contractual or as a 10-and-5, it creates additional difficulties for all of us to complete trades, because once there is a window of opportunity for stuff to get out, it's out. It just does. That's the way it is in today's world."
Dempster leads the Major Leagues with a 2.11 ERA in 15 games, and his next scheduled start is Wednesday against the Pirates.
Zack Greinke has been at the top of the Braves' wish list over the past month. But with hopes of potentially keeping Greinke, the Brewers are asking for a significant return that would include Teheran and at least one other highly regarded prospect.
With that kind of asking price, the Braves will be more interested in attempting to sign Greinke as a free agent next winter.