The Cubs and Braves had a deal in place, in which Dempster would go to Atlanta in exchange for 22-year-old pitcher Randall Delgado. However, Dempster has the right to veto any deal as a player with 10 years in the Major Leagues and five with the same team.
In an interview on 680-AM The Fan in Atlanta, Wren said it was "highly unlikely" the Braves would get Dempster.
"We put parameters on the deal that expired [Tuesday]," Wren said. "We were moving on from the time we heard that there was the potential of another club being really where he wanted to go. And he had a lot of personal reasons for that.
"We haven't stopped pursuing other pitchers," Wren said. "We've had scouts in ballparks seeing everyone. It's one of those bumps in the road, but at the same time we put parameters on it that expired yesterday, so we've moved on."
Cubs assistant general manager Randy Bush would not comment on Wren's statements, saying, "We can let his comments stand."
Dempster gave Cubs president of baseball operations Theo Epstein and general manager Jed Hoyer a list of which teams he would prefer, and the pitcher said the front office has kept him informed throughout the process.
The Dodgers were reportedly still pursuing Dempster, who would be reunited with friend Ted Lilly on their staff.
"It's awesome being the hammer and not the nail," Dempster said after his last start, on Friday against the Cardinals.
There were reports that Dempster was "blindsided" by the Braves deal, but sources told MLB.com that Dempster knew about the proposal, and the surprise was how public the trade became before he had made his decision.
"It just makes it harder [to make a decision] when something that wasn't supposed to be public knowledge becomes public knowledge, especially before I even knew it was public knowledge," Dempster said. "That's when things start to get harder, when you get everybody's opinions of what was going on, and really wasn't what went on or what took place, so you don't get to focus your full attention on what you're trying to do and you have to focus on everybody else's perception of what's going on."
Because Dempster will be a free agent at the end of the year and players must be with a team for an entire season in order to qualify for Draft-pick compensation, according to the new Collective Bargaining Agreement, the Braves understood that a deal could possibly benefit them for only the next few months. The righty has not requested a contract extension as a condition for a trade but did admit that anybody would be looking for some security.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter@CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.