"I think it's very highly unlikely," Wren said on "The Rude Awakening" on 680-AM The Fan in Atlanta. "We put parameters on the deal that expired (Tuesday). 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. 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."
After picking up the loss in a 3-2 decision against the Pittsburgh Pirates on Wednesday, Dempster said he understands the Braves' need to explore other options. He also said he hasn't ruled out going to the Braves if another deal is forged by Tuesday's 4 p.m. ET trade deadline.
"If that's still an option down the road, then it's something I'm going to have to look at, but I'm going to try and make the best decision for me and my family," Dempster said. "I'm going to take a plane ride (back to Chicago) and enjoy my off day tomorrow if that's possible. And then I'll see where I'm at from there."
A major league source told ESPNChicago.com's Doug Padilla that the Cubs respect and understand the Braves' desire to move on, but sources tell ESPN The Magazine's Buster Olney that the Cubs are hoping Dempster changes his mind about the deal to send him to Atlanta.
Sources also tell Olney the Cubs are not close to a deal sending Dempster to the Los Angeles Dodgers, who are considered Dempster's first choice, and the Cubs might keep Dempster and make an offer that qualifies for a compensation draft pick if he doesn't re-sign.
Assistant Cubs general manager Randy Bush, the highest-ranking front-office member in Pittsburgh with the club, declined to talk specifically about the collapsed deal with the Braves.
"I don't want to comment on that," Bush said. "Frank, certainly we can let his comments stand."
Reports surfaced Monday that the Cubs and Braves had agreed to a deal that would send Dempster to Atlanta for 22-year-old starter Randall Delgado. All that was needed was approval from Dempster, who has veto power over any trade. He said Tuesday that he was in no hurry to make a decision. Dempster reportedly has the Dodgers as his top choice with the Braves next on the list.
"I want to look everything over first before I make any decisions and I have time to do that," Dempster said Tuesday. "There's a week before the trading deadline. That's where I stand on it."
Would the Braves go through with the trade if Dempster gave his approval in the next few days?
"I'm not going to paint us in a corner one way or another," Wren said. "Let's just say that we have moved on. We're looking for impact pitching, someone that can make a difference for us as we go down the stretch the last two months."
Dempster said he knew nothing about the deal when word spread on Twitter on Monday afternoon, downplaying the reports as "speculation." A source told ESPN.com senior MLB writer Jerry Crasnick that Dempster was unhappy that word of the deal got out before he was informed by the Cubs.
"I don't think players ever get a heads up on deals," Wren said. "I mean, it just doesn't work that way. In his case, from my understanding, and I'm only getting it secondhand from the Cubs, they had a meeting with him a couple of weeks ago and laid it out and that the primary two suitors were us and the Dodgers. He had positive things to say about both, but he had a slight preference to the Dodgers because of Ted Lilly. He and Ted Lilly are best of friends, and he'd like to go play with his friend. I think there were also some personal issues that suited better for him.
"As it went down, from my understanding, the Cubs informed him over the last week that the Dodgers weren't really as aggressive as we were, and they thought the deal was going to go with us. I think he was given a heads up along the way. I think it may be the way it was presented as far as coming out in the media. I think that was the blindsiding, not that he didn't necessarily that he didn't know it was coming down."
Dempster said Tuesday that he understands an unfortunate side effect of waiting to approve a deal means he will alienate a segment of the Cubs' fan base.
"That's fine; people can say what they want to say," Dempster said. "All I know is that when I put my uniform on, I give 100 percent to the Cubs, and I think that's all you can really ask whether you are a player, a coach, in the front office or a fan of the team. If all the players did that, you'd be pretty happy."
A tumultuous few days seemed to get to Dempster on Wednesday. After learning he would not return to the game in the seventh, he threw a drink cooler to the ground and threw his own drink against the wall before going into the clubhouse.
Cubs starter Paul Maholm, who's also been the subject of trade speculation, said Dempster has handled the situation in an "awesome" manner.
"He has that right (to veto a trade), and he's going to do what's best for himself and his family," Maholm said Wednesday on "The Waddle & Silvy Show" on ESPN 1000. "Obviously, he's a die-hard Cub, so we'll see. ... It's fun playing with him and fun being around him. Hopefully we'll get to play for a while together.
"He's about as true a professional as you can be. He kind of laughed about it. There are rumors out there, but when you talk to him, you're kind of getting it straight from the source, so we'll just see."
If the Cubs keep Dempster and make him an offer, the offer would have to be an average of the top 50 salaries in baseball, which at this point is $12.2 million. The offer would have to be made right before the free-agent period begins, which is immediately after the World Series ends. If it's accepted, it's a one-year contract, and all of his rights from his previous contract -- such as his 10-5 veto rights -- stay intact.
If he signs with another team, the Cubs would get a sandwich pick between the first and second rounds of the draft.
ESPNChicago.com's Doug Padilla and Bruce Levine contributed to this report.