If a vast majority of teams in playoff contention covet starting pitching, then Ryan Dempster has to be one of the most valuable assets on the block. The Atlanta Braves have glaring holes in their rotation to fill, so it would seem to be a natural fit. 
According to Ken Rosenthal of Fox Sports, Dempster does have the Braves high on his list of preferred teams to go to. 
Ryan Dempster’s first choice is the Los Angeles Dodgers and his second is the Atlanta Braves, according to major league sources.
Whether the veteran right-hander would allow the Cubs to trade him to another team could be determined in the next several days.
Dempster, as a player with 10 years of service, the last five with the same team, has the right to veto any deal.
Looking at Dempster's numbers, there is some regression that will come the rest of the season. His home-run rate (0.59), batting average on balls in play (.242) and left-on-base percentage (85.5) are all abnormally low. 

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That said, even if his numbers do start to level off over the final two months of the season, Dempster would probably be the No. 1 or No. 2 starter for the Braves right now.
They have lost Brandon Beachy for the year and have reached out to Ben Sheets, who hadn't pitched in a big league game since 2010. Mike Minor has been a disaster. Tommy Hanson keeps taking steps back, and his velocity keeps going down. 
At least Dempster would give them more stability after Tim Hudson in the rotation. And for all their starting pitching problems, the Braves are still just 4.5 games behindWashington in the National League East and hold the second Wild Card spot right now. 
It will be interesting to see what the Braves would have to give up to get Dempster, as he is performing well right now but is coming off an injury earlier this season. 
The Braves do need help. Dempster apparently likes them a lot. It would seem to be a natural fit, if they can figure out how to make a deal work with Chicago.