Yet there are likely plenty of teams also paying attention to the best stretch of Paul Maholm's career.
Maholm will try become the first Cubs left-hander in five seasons to win six consecutive starts Sunday when his team's series concludes with the St. Louis Cardinals.
Little was expected of the Cubs (41-58) this season, but new team president Theo Epstein and general manager Jed Hoyer arrived with big plans to rebuild a franchise that hasn't won a playoff game in nine years.
Dempster and Garza were thought to have the greatest trade value, but Dempster has been flexing his 10-and-5 veto rights and Garza's triceps injury could hurt Chicago's chances of getting equal return in a deal.
The Cubs, though, may have caught a break with Maholm (9-6, 3.88 ERA) pitching so well the last four weeks. The left-hander has a 0.96 ERA during his five-start streak after striking out seven in eight innings of Tuesday's 5-1 win at Pittsburgh.
"He's been great,'' manager Dale Sveum said. "He's working in all four pitches and throwing them for strikes. He's not giving in to the other team. He's not doing anything he shouldn't be doing. He's well prepared and is executing his game plan."
There is plenty of speculation about where Maholm may end up, but his concern is the Cardinals (54-47). He is 0-1 with a 9.00 ERA in two starts against them this season.
"I know there are some (rumors) out there but I signed to pitch with the Cubs and I'm not thinking about other teams,'' said Maholm, who could become the first Cubs southpaw to win six straight starts since Ted Lilly from June 26-July 25, 2007. "I like the team I'm with. I've enjoyed playing in Chicago this season. I guess we'll see what happens in the next week.''
The Cubs, winners of 11 of 14 at home, will face Adam Wainwright (8-10, 4.31) for the third time this season after snapping St. Louis' four-game winning streak and a five-game skid in this Central matchup with Saturday's 3-2 victory.
The St. Louis right-hander is 0-1 with a 9.00 ERA against the Cubs this season after recording seven strikeouts in six strong innings of a 3-2, 10-inning loss April 24. Wainwright, the 2010 NL Cy Young runner-up, had won his previous five starts on the North Side - all coming prior to his elbow surgery that sidelined him in 2011.
Cardinals third baseman David Freese, who is batting .571 (16 for 28) during a nine-game hitting streak, is expected to see his first action of the series after sitting out with cramping in his right calf. Last season's NLCS and World Series MVP has two hits - including a homer - in 11 at-bats versus Maholm.
Left fielder Matt Holliday, 18 for 52 with five homers and 10 RBIs off Cubs pitching this season, is 6 for 29 with three homers against the left-hander.
Cubs left fielder Alfonso Soriano - 3 for 5 with a double against Wainwright this season - has seven RBIs in the last four contests.
St. Louis has won eight of 13 versus Chicago and can clinch the season series with a victory.