The deal, a source told ESPN.com MLB Insider Keith Law, would send Atlanta right-hander Randall Delgado to Chicago in exchange for Dempster.
Dempster has refuted the deal on his foundation's official Twitter account: "THERE IS NO TRADE dont know where this info came from!"
"I found out about it when I came off the field after early (batting practice)," Cubs manager Dale Sveum said Monday. "Somebody said they saw it on the website. So I got on the website and saw it and called the higher-ups to make sure. And they were like, 'No, nothing is happening. I don't know where that came from.' That's where we are with that."
Cubs assistant general manager Randy Bush said, "There is nothing to report."
One source familiar with the discussions told ESPN.com's Jayson Stark on Tuesday that the status of the deal should be resolved "shortly."
Dempster, 35, has 10-5 trade protection rights, meaning he must approve any trade before it can be executed. The right-hander arrived in the Cubs clubhouse at PNC Park on Monday and addressed the trade talk, downplaying it as "speculation."
"I don't want to talk about speculation," Dempster said.
Dempster also said he became aware of the planned trade after waking up from a nap Monday afternoon. He claimed that he still plans on making his next scheduled start for the Cubs on Wednesday against the Pittsburgh Pirates.
A source told ESPN.com senior MLB writer Jerry Crasnick that Dempster is unhappy that reports of a deal got out before he was informed by the Cubs. The source also said Dempster will now take a day or two to ponder whether he will accept a deal to the Braves.
"I know what you guys know, basically the same thing, maybe a little bit more. I'm not going to lie to you about that," Braves manager Fredi Gonzalez told the team's official website after Monday's game. "But that's all I know right now. We're in a holding pattern."
Dempster is in the final year of his contract with the Cubs and widely is considered one of the top starting pitchers available on the trade market. The right-hander leads the majors with a 2.11 ERA and recently reeled off 33 consecutive scoreless innings.
The Cubs were still talking to both the Braves and Dodgers about Ryan Dempster today, sources said, because Dempster still hasn't agreed to waive his no-trade clause to accept his trade to Atlanta.
A 15-year veteran, Dempster is 5-4 in 15 starts this season, his ninth with the Cubs. Dempster's scoreless-innings streak was snapped in the opening frame of Friday's loss to the St. Louis Cardinals.
Dempster would help stabilize and improve a Braves rotation that has struggled to replace Brandon Beachy, who suffered a season-ending elbow injury last month.
Delgado, 22, is 4-9 with a 4.42 ERA in 17 starts this season. The right-hander entered 2012 as the Braves' No. 3 overall prospect, according to Baseball America.
Atlanta trails the first-place Washington Nationals by 3½ games in the NL East and remains in contention for a wild-card spot despite a starting rotation that includes Delgado and fellow youngster Mike Minor.
The Braves have been bolstered by the re-emergence of right-hander Ben Sheets, who has thrown 12 scoreless innings over two starts. Sheets, 34, had not pitched in the majors since 2010 because of an elbow injury.
ESPN.com senior writers Jayson Stark and Jerry Crasnick, ESPNChicago.com's Doug Padilla and The Associated Press contributed to this report.