Dempster (5-5, 2.25 ERA) is on track to make his next start on Tuesday, which would be just a few hours after the Trade Deadline. He's been one of the top targets this season.
"I think there's no question it's going to weigh on you a little bit," Cubs manager Dale Sveum said of the distractions created by the rumors. "Everybody's human."
Whether Dempster goes is his call. He has 10 years in the big leagues and five with the same team, which allows him veto power over any deal. That may sound selfish, but it's the players' rights.
"Fortunately for Dempster, he's got the 10-and-5 rights, and for whatever reason, people don't know what's going on behind the scenes and all the reasons why you accept and why you don't," Sveum said. "It's an unfortunate thing that [people] jump to conclusions. He's one of the most class guys you'll ever be around and [a good] teammate, and obviously [he's] very productive when he goes out there every five days, too. It's one of those things where you're good if you do, good if you don't, and it's a tough situation to be in."
Sveum isn't pushing for a trade.
"We're only going to be a better team with him on the field all year," Sveum said.
Dempster and Sveum didn't agree on Wednesday, which was Dempster's last start. He was pulled after 93 pitches over six innings, and trailing, 3-2, against the Pirates. Dempster threw a cooler lid, then slammed the cooler and threw a water bottle in the dugout.
The two talked later.
"Players have the right to do things and snap, and those things happen," Sveum said. "It's not all just because of one thing or because he got taken out of a game. It's a very competitive sport and there's a lot of reasons why some guys all of a sudden don't have a good day. We had a good talk, and everything's good."
Tuesday's Trade Deadline can't come soon enough for Sveum.
"It's something that's there and we know it's part of the game," he said. "I don't care who you are, you want to move on to other questions, there's no question about it."
Sveum has been in touch with Cubs president of baseball operations Theo Epstein and general manager Jed Hoyer.
"We talk, and we talk about a lot of things and it's basically kind of, 'I don't really want to know until it's a sealed deal,'" Sveum said.