Dempster, 35, rumored to be dealt by the Deadline, said Cubs president of baseball operations Theo Epstein and general manager Jed Hoyer have kept him up to date when necessary. The Braves thought they had a deal last week, but the Dodgers appear to have the most interest.
"If they have anything that comes to fruition, [I asked them to] just let me know and we'll make a decision from there," Dempster said. "Nothing's been said in a little while."
Dempster (5-5, 2.25 ERA) has control over where he would go because he has 10-and-5 rights (10 years in the big leagues, five with the same team). Even though he'll make the final call, all the rumors have become a little tiring.
"I'm human, so it's an emotional roller coaster sometimes," he said, "but at the same time, I can control what I do, and I'm going to try to do the best job of that. I have a job to do [Tuesday] and that's to go out there and pitch, and I"m trying to prepare for that."
Asked if he had a gut feeling about what might happen, Dempster said, "I have all kinds of gut feelings right now."
He's gotten positive feedback from fans at Wrigley Field, who don't want to lose the right-hander.
"I'm truly grateful for that," Dempster said.
What has made Dempster so effective this season has been his pitch efficiency, Sveum said. The right-hander added a backdoor cutter, which has given him a fourth pitch, and he can locate well. He's third in the NL in WHIP at 1.04 and is holding opponents to a .210 average. He has posted a quality start in 11 of his 16 starts and would have more wins if not for a lack of run support early. He didn't win his first game until June 5.
In 1996, when Dempster was in the Rangers' Minor League system, he was traded to the Marlins, and in 2002, he was dealt to the Reds. Getting traded isn't a first, but it's still been strange to hear his name mentioned so often on the clubhouse television.
"There's tons of rumors and tons of speculation all the time," Dempster said. "This is something I've tried to keep close to me so it can get handled the best it can. Sometimes there are rumors that are true, and sometimes there are rumors that aren't [true]. I can't control that. I can just control what I can do, and that's go out there and prepare to do my job the best I can."
What if the Cubs don't make a deal?
"It's a great place to play," Dempster said of Chicago. "I've enjoyed every moment I've played here, and I'm super proud to be a Chicago Cub and I understand that's always a possibility, and if that's the case, I'm going to give everything I have starting [Tuesday] night. Whatever ends up happening in 24 hours or 23 hours from now, we'll find out then. It could be sooner, it could be wearing my uniform and going out and pitching [Tuesday]."