The deal, as proposed, was going to send top Braves pitching prospect Randall Delgado to the Cubs.
"It could happen, or it could blow up,'' another person said.
It isn't clear what the holdup is, as several sources suggested the trade was on the verge of happening earlier in the day.
In any case, the momentum for the deal is said to have slowed quite a bit.
On Monday afternoon it appeared the deal was about to go down, but the Cubs said no announcement was planned, and Dempster later tweeted that "there is no trade'' on his twitter account.
Dempster has 10-and-5 veto right but it isn;t clear that that has anything to do with the holdup. Dempster tweeted in mid-afternoon that there was "no trade.''